David Osten awarded with internship at the German Bundestag from Heraeus Foundation

Here is a list of my publications and theses. Most of them can also be found on inspire-HEP or the arXiv. The citation counts shown here are based on the inSPIRE database. Please contact me if you have any questions or comments concerning my work.


F. Hassler, Y. Sakatani, L. Scala: Generalized Dualities for Heterotic and Type I Strings, preprint December 2023, arXiv:2312.16283, abstract, Citations: 1

We define generalized dualities for heterotic and type I strings based on consistent truncations to half-maximal gauged supergravities in more than three dimensions. The latter are constructed from a generalized Scherk-Schwarz ansatz in heterotic double field theory that satisfies the strong constraint. Necessary and sufficient conditions on the resulting embedding tensor are discussed, showing that only certain gaugings, called geometric, can arise from this procedure. For all of them, we explicitly construct the internal geometry and gauge potentials. In general, this construction is not unique and permits different uplifts which are used to define generalized T-duality. Two examples are worked out underlying the utility of our approach to explore new dualities and uplifts of half-maximal gauged supergravities.

F. Hassler, Y. Sakatani: The Hierarchy of Curvatures in Exceptional Geometry, preprint November 2023, arXiv:2311.12095, abstract, Citations: 2

Despite remarkable success in describing supergravity reductions and backgrounds, generalized geometry and the closely related exceptional field theory are still lacking a fundamental object of differential geometry, the Riemann tensor. We explain that to construct such a tensor, an as of yet overlooked hierarchy of connections is required. They complement the spin connection with higher representations known from the tensor hierarchy of gauged supergravities. In addition to solving an important conceptual problem, this idea allows to define and explicitly construct generalized homogeneous spaces. They are the underlying structures of generalized U-duality, admit consistent truncations and provide a huge class of new backgrounds for flux compactifications with non-trivial generalized structure groups.

F. Hassler, S. Lacroix, B. Vicedo: The Magic Renormalisability of Affine Gaudin Models, JHEP 12 (2023), arXiv:2310.16079, abstract, Citations: 4

We study the renormalisation of a large class of integrable σ\sigma-models obtained in the framework of affine Gaudin models. They are characterised by a simple Lie algebra g\mathfrak{g} and a rational twist function φ(z)\varphi(z) with simple zeros, a double pole at infinity but otherwise no further restrictions on the pole structure. The crucial tool used in our analysis is the interpretation of these integrable theories as E\mathcal{E}-models, which are σ\sigma-models studied in the context of Poisson-Lie T-duality and which are known to be at least one- and two-loop renormalisable. The moduli space of E\mathcal{E}-models still contains many non-integrable theories. We identify the submanifold formed by affine Gaudin models and relate its tangent space to curious matrices and semi-magic squares. In particular, these results provide a criteria for the stability of these integrable models under the RG-flow. At one loop, we show that this criteria is satisfied and derive a very simple expression for the RG-flow of the twist function, proving a conjecture made earlier in the literature.

Daniel Butter, Falk Hassler, Christopher N. Pope, Haoyu Zhang: Generalized Dualities and Supergroups, JHEP 12 (2023), arXiv:2307.05665, abstract, Citations: 3

Using a recently developed formulation of double field theory in superspace, the graviton, BB-field, gravitini, dilatini, and Ramond-Ramond bispinor are encoded in a single generalized supervielbein. Duality transformations are encoded as orthosymplectic transformations, extending the bosonic O(DD,DD) duality group, and these act on all constituents of the supervielbein in an easily computable way. We first review conventional non-abelian T-duality in the Green-Schwarz superstring and describe the dual geometries in the language of double superspace. Since dualities are related to super-Killing vectors, this includes as special cases both abelian and non-abelian fermionic T-duality. We then extend this approach to include Poisson-Lie T-duality and its generalizations, including the generalized coset construction recently discussed in arXiv:1912.11036. As an application, we construct the supergeometries associated with the integrable λ\lambda and η\eta deformations of the AdS5×_5 \timesS5^5 superstring. The deformation parameters λ\lambda and η\eta are identified with the possible one-parameter embeddings of the supergravity frame within the doubled supergeometry. In this framework, the Ramond-Ramond bispinors are directly computable purely from the algebraic data of the supergroup.

F. Hassler, Y. Sakatani: All maximal gauged supergravities with uplift, Prog. Theor. Exp. Phys. 2023 (2023), arXiv:2212.14886, abstract, Citations: 7

Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations and dualities, which is not immediately obvious. A prime example is generalised Scherk-Schwarz reductions in double field theory, which have been shown to be in one-to-one correspondence with Poisson-Lie T-duality. Here we demonstrate that this relation is only the tip of the iceberg. Currently, the most general known classes of T-dualities (excluding mirror symmetry) are based on dressing cosets. But as we discuss, they can be further extended to the even larger class of generalised cosets. We prove that the latter give rise to consistent truncations for which the ansatz can be constructed systematically. Hence, we pave the way for many new examples of T-dualities and consistent truncations. The arising structures result in covariant tensors with more than two derivatives and we argue how they might be key to understand generalised T-dualities and consistent truncations beyond the leading two derivative level.

D. Butter, F. Hassler, C. Pope, H. Zhang: Consistent Truncations and Dualities, JHEP 4 (2023), arXiv:2211.13241, abstract, Citations: 5

Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations and dualities, which is not immediately obvious. A prime example is generalised Scherk-Schwarz reductions in double field theory, which have been shown to be in one-to-one correspondence with Poisson-Lie T-duality. Here we demonstrate that this relation is only the tip of the iceberg. Currently, the most general known classes of T-dualities (excluding mirror symmetry) are based on dressing cosets. But as we discuss, they can be further extended to the even larger class of generalised cosets. We prove that the latter give rise to consistent truncations for which the ansatz can be constructed systematically. Hence, we pave the way for many new examples of T-dualities and consistent truncations. The arising structures result in covariant tensors with more than two derivatives and we argue how they might be key to understand generalised T-dualities and consistent truncations beyond the leading two derivative level.

R. Borsato, S. Driezen, F. Hassler: An Algebraic Classification of Solution Generating Techniques, Phys. Lett. B 823 (2021), arXiv:2109.06185, abstract, Citations: 19

We consider a two-fold problem: on the one hand, the classification of a family of solution-generating techniques in (modified) supergravity and, on the other hand, the classification of a family of canonical transformations of 2-dimensional σ\sigma-models giving rise to integrable-preserving transformations. Assuming a generalised Scherk-Schwarz ansatz, in fact, the two problems admit essentially the same algebraic formulation, emerging from an underlying double Lie algebra d\mathfrak d. After presenting our derivation of the classification, we discuss in detail the relation to modified supergravity and the additional conditions to recover the standard (unmodified) supergravity. Starting from our master equation - that encodes all the possible continuous deformations allowed in the family of solution-generating techniques - we show that these are classified by the Lie algebra cohomologies H2(h,R)H^2(\mathfrak h,\mathbb R) and H3(h,R)H^3(\mathfrak h,\mathbb R) of the maximally isotropic subalgebra h\mathfrak h of the double Lie algebra d\mathfrak d. We illustrate our results with a non-trivial example, the bi-Yang-Baxter-Wess-Zumino model.

F. Hassler, C. N. Pope, H. Zhang: Double Field Theory and Pseudo-Supersymmetry, Phys. Rev. D 104 (2020), arXiv:2012.12278, abstract

Supersymmetric bosonic backgrounds governed by first-order BPS equations, can be realised in a much broader setting by relaxing the requirement of closure of the superalgebra beyond the level of quadratic fermion terms. The resulting pseudo-supersymmetric theories can be defined in arbitrary spacetime dimensions. We focus here on the N=1\mathcal{N}=1 pseudo-supersymmetric extensions of the arbitrary-dimensional bosonic string action, which were constructed a few years ago. In this paper, we recast these in the language of generalised geometry. More precisely, we construct the action and the corresponding supersymmetry transformation rules in terms of O(DD)×O(DD) covariant derivatives, and we discuss consistent truncations on manifolds with generalised GG-structure. As explicit examples, we discuss Minkowski×GG vacuum solutions and their corresponding pseudo-supersymmetry. We also briefly discuss squashed group manifold solutions, including an example with a Lorentzian signature metric on the group manifold GG.

F. Hassler, T. B. Rochais: O(DD,DD)-covariant two-loop β\beta-functions and Poisson-Lie T-duality, JHEP 10 (2021), arXiv:2011.15130, abstract, Citations: 18

We show that the one- and two-loop β\beta-functions of the closed, bosonic string can be written in a manifestly O(DD,DD)-covariant form. Based on this result, we prove that 1) Poisson-Lie symmetric σ\sigma-models are two-loop renormalisable and 2) their β\beta-functions are invariant under Poisson-Lie T-duality. Moreover, we identify a distinguished scheme in which Poisson-Lie symmetry is manifest. It simplifies the calculation of two-loop β\beta-functions significantly and thereby provides a powerful new tool to advance into the quantum regime of integrable σ-models and generalised T-dualities. As an illustrating example, we present the two-loop β\beta-functions of the integrable η\eta- and λ\lambda-deformation.

F. Hassler, T. Rochais: α\alpha'-Corrected Poisson-Lie T-Duality, Fortsch. Phys. 68 (2020), arXiv:2007.07897, abstract, Citations: 34

We propose leading order α\alpha'-corrections to the Poisson-Lie T-duality transformation rules of the metric, BB-field, and dilaton. Based on Double Field Theory, whose corrections to this order are known, we argue that they map conformal field theories to conformal field theories. Remarkably, Born geometry plays a central role in the construction.

S. Demulder, F. Hassler, G. Piccinini, D. C. Thompson: Integrable deformation of CPn\mathbb{CP}^n and generalised Kähler geometry, JHEP 10 (2020), arXiv:2002.11144, abstract, Citations: 15

We build on the results of arXiv:1912.11036 for generalised frame fields on generalised quotient spaces and study integrable deformations for CPn\mathbb{CP}^n. In particular we show how, when the target space of the Principal Chiral Model is a complex projective space, a two-parameter deformation can be introduced in principle. The second parameter can however be removed via a diffeomorphism, which we construct explicitly, in accordance with the results stemming from a thorough integrability analysis we carry out. We also elucidate how the deformed target space can be seen as an instance of generalised Kaehler, or equivalently bi-Hermitian, geometry. In this respect, we find the generic form of the pure spinors for CPn and the explicit expression for the generalised Kaehler potential for nn=1,2.

S. Demulder, F. Hassler, G. Piccinini, D. C. Thompson: Generalised Cosets, JHEP 09 (2021), arXiv:1912.11036, abstract, Citations: 20

Recent work has shown that two-dimensional non-linear σ\sigma-models on group manifolds with Poisson-Lie symmetry can be understood within generalised geometry as exemplars of generalised parallelisable spaces. Here we extend this idea to target spaces constructed as double cosets M=G~\D/HM=\widetilde{G}\backslash D/H. Mirroring conventional coset geometries, we show that on MM one can construct a generalised frame field and a HH-valued generalised spin connection that together furnish an algebra under the generalised Lie derivative. This results naturally in a generalised covariant derivative with a (covariantly) constant generalised intrinsic torsion, lending itself to the construction of consistent truncations of 10-dimensional supergravity compactified on MM. An important feature is that MM can admit distinguished points, around which the generalised tangent bundle should be augmented by localised vector multiplets. We illustrate these ideas with explicit examples of two-dimensional parafermionic theories and NS5-branes on a circle.

F. Hassler, J. J. Heckman, T. B. Rochais, T. Rudelius, H. Y. Zhang: T-Branes, String Junctions, and 6D SCFTs, Phys. Rev. D 101 (2019), arXiv:1907.11230, abstract, Citations: 32

Recent work on 6D superconformal field theories (SCFTs) has established an intricate correspondence between certain Higgs branch deformations and nilpotent orbits of flavor symmetry algebras associated with T-branes. In this paper, we return to the stringy origin of these theories and show that many aspects of these deformations can be understood in terms of simple combinatorial data associated with multi-pronged strings stretched between stacks of intersecting 7-branes in F-theory. This data lets us determine the full structure of the nilpotent cone for each semi-simple flavor symmetry algebra, and it further allows us to characterize symmetry breaking patterns in quiver-like theories with classical gauge groups. An especially helpful feature of this analysis is that it extends to "short quivers" in which the breaking patterns from different flavor symmetry factors are correlated.

F. Hassler, D. Lüst, F. J. Rudolph: Para-Hermitian Geometries for Poisson-Lie Symmetric σ\sigma-models, JHEP 10 (2019), arXiv:1905.03791, abstract, Citations: 28

The doubled target space of the fundamental closed string is identified with its phase space and described by an almost para-Hermitian geometry. We explore this setup in the context of group manifolds which admit a maximally isotropic subgroup. This leads to a formulation of the Poisson-Lie σ\sigma-model and Poisson-Lie T-duality in terms of para-Hermitian geometry. The emphasis is put on so called half-integrable setups where only one of the Lagrangian subspaces of the doubled space has to be integrable. Using the dressing coset construction in Poisson-Lie T-duality, we extend our construction to more general coset spaces. This allows to explicitly obtain a huge class of para-Hermitian geometries. Each of them is automatically equipped which a generalized frame field, required for consistent generalized Scherk-Schwarz reductions. As examples we present integrable λ\lambda- and η\eta-deformations on the three- and two-sphere.

F. Hassler: RG flow of integrable E\mathcal{E}-models, Phys. Lett. B 818 (2021), arXiv:2012.10451, abstract, Citations: 16

We compute the one- and two-loop RG flow of integrable σ\sigma-models with Poisson-Lie symmetry. They are characterised by a twist function with 2N2N simple poles/zeros and a double pole at infinity. Hence, they capture many of the known integrable deformations in a unified framework, which has a geometric interpretation in terms of surface defects in a 4D Chern-Simons theory. We find that these models are one-loop renormalisable and present a very simple expression for the flow of the twist function. At two loops only models with N=1N=1 are renormalisable. Applied to the λ\lambda-deformation on a semisimple group manifold, our results reproduce the β\beta-functions in the literature.

S. Demulder, F. Hassler, D. C. Thompson: Doubled aspects of generalised dualities and integrable deformations, JHEP 02 (2019), arXiv:1810.11446, abstract, Citations: 83

The worldsheet theories that describe Poisson-Lie T-dualisable σ\sigma-models on group manifolds as well as integrable η\eta, λ\lambda and β\beta-deformations provide examples of E\mathcal{E}-models. Here we show how such E\mathcal{E}-models can be given an elegant target space description within Double Field Theory by specifying explicitly generalised frame fields forming an algebra under the generalised Lie derivative. With this framework we can extract simple criteria for the R/R fields and the dilaton that extend the E\mathcal{E}-model conditions to type II backgrounds. In particular this gives conditions for a type II background to be Poisson-Lie T-dualisable. Our approach gives rise to algebraic field equations for Poisson-Lie symmetric spacetimes and provides an effective tool for their study.

F. Apruzzi, F. Hassler, J. J. Heckman, T. B. Rochais: Nilpotent Networks and 4D RG Flows, JHEP 05 (2019), arXiv:1808.10439, abstract, Citations: 17

Starting from a general N=2\mathcal{N}=2 SCFT, we study the network of N=1\mathcal{N}=1 SCFTs obtained from relevant deformations by nilpotent mass parameters. We also study the case of flipper field deformations where the mass parameters are promoted to a chiral superfield, with nilpotent vev. Nilpotent elements of semi-simple algebras admit a partial ordering connected by a corresponding directed graph. We find strong evidence that the resulting fixed points are connected by a similar network of 4D RG flows. To illustrate these general concepts, we also present a full list of nilpotent deformations in the case of explicit N=2\mathcal{N}=2 SCFTs, including the case of a single D3-brane probing a DD- or EE-type FF-theory 7-brane, and 6D (GG,GG) conformal matter compactified on a T2, as described by a single M5-brane probing a DD- or EE-type singularity. We also observe a number of numerical coincidences of independent interest, including a collection of theories with rational values for their conformal anomalies, as well as a surprisingly nearly constant value for the ratio aIRa_{\mathrm{IR}}/cIRc_{\mathrm{IR}} for the entire network of flows associated with a given UV N=2\mathcal{N}=2 SCFT. The arXiv submission also includes the full dataset of theories which can be accessed with a companion Mathematica script.

F. Hassler, J. J. Heckman: Punctures and Dynamical Systems, Lett. Math. Phys. 109 (2019), arXiv:1711.03973, abstract, Citations: 10

With the aim of better understanding the class of 4D theories generated by compactifications of 6D superconformal field theories (SCFTs), we study the structure of N = 1 supersymmetric punctures for class SΓS_\Gamma theories, namely the 6D SCFTs obtained from M5-branes probing an ADE singularity. For M5-branes probing a C2/ZkC^2 / Z_k singularity, the punctures are governed by a dynamical system in which evolution in time corresponds to motion to a neighboring node in an affine A-type quiver. Classification of punctures reduces to determining consistent initial conditions which produce periodic orbits. The study of this system is particularly tractable in the case of a single M5-brane. Even in this "simple" case, the solutions exhibit a remarkable level of complexity: Only specific rational values for the initial momenta lead to periodic orbits, and small perturbations in these values lead to vastly different late time behavior. Another difference from half BPS punctures of class S theories includes the appearance of a continuous complex "zero mode" modulus in some puncture solutions. The construction of punctures with higher order poles involves a related set of recursion relations. The resulting structures also generalize to systems with multiple M5-branes as well as probes of D- and E-type orbifold singularities.

F. Hassler: Poisson-Lie T-Duality in Double Field Theory, Phys. Lett. B 807 (2020), arXiv:1707.08624, abstract, Citations: 99

We present a formulation of Double Field Theory with a Drinfeld double as extended spacetime. It makes Poisson-Lie T-duality (including abelian and non-abelian T-duality as special cases) manifest. This extends the scope of possible applications of the theory, which so far captured abelian T-duality only, considerably. The full massless bosonic subsector (NS/NS and R/R) of type II string theories is covered.

P. du Bosque, F. Hassler, D. Lüst: Generalized Parallelizable Spaces from Exceptional Field Theory, JHEP 01 (2018), arXiv:1705.09304, abstract, Citations: 18

Generalized parallelizable spaces allow a unified treatment of consistent maximally supersymmetric truncations of ten- and eleven-dimensional supergravity in generalized geometry. Known examples are spheres, twisted tori and hyperboloides. They admit a generalized frame field over the coset space MM=G/HG/H which reproduces the Lie algebra g\mathfrak{g} of GG under the generalized Lie derivative. An open problem is a systematic construction of these spaces and especially their generalized frames fields. We present a technique which applies to dimM\dim M=4 for SL(5) exceptional field theory. In this paper the group manifold GG is identified with the extended space of the exceptional field theory. Subsequently, the section condition is solved to remove unphysical directions from the extended space. Finally, a SL(5) generalized frame field is constructed from parts of the left-invariant Maurer-Cartan form on GG. All these steps impose conditions on GG and HH.

F. Hassler: The Topology of Double Field Theory, JHEP 04 (2018), arXiv:1611.07978, abstract, Citations: 39

We describe the doubled space of Double Field Theory as a group manifold GG with an arbitrary generalized metric. Local information from the latter is not relevant to our discussion and so GG only captures the topology of the doubled space. Strong Constraint solutions are maximal isotropic submanifold MM in GG. We construct them and their Generalized Geometry in Double Field Theory on Group Manifolds. In general, GG admits different physical subspace MM which are T-dual to each other. By studying two examples, we reproduce the topology changes induced by T-duality with non-trivial HH-flux which were discussed by Bouwknegt, Evslin and Mathai [hep-th/0306062].

F. Apruzzi, F. Hassler, J. J. Heckman, I. V. Melnikov: From 6D SCFTs to Dynamic GLSMs, Phys. Rev. D96 (2017), arXiv:1610.00718, abstract, Citations: 44

Compactifications of 6D superconformal field theories (SCFTs) on four-manifolds generate a large class of novel 2d quantum field theories. We consider in detail the case of the rank one simple non-Higgsable cluster 6D SCFTs. On the tensor branch of these theories, the gauge group is simple and there are no matter fields. For compactifications on suitably chosen Kahler surfaces, we present evidence that this provides a method to realize 2d SCFTs with N = (0,2) supersymmetry. In particular, we find that reduction on the tensor branch of the 6D SCFT yields a description of the same 2d fixed point that is described in the UV by a gauged linear sigma model (GLSM) in which the parameters are promoted to dynamical fields, that is, a "dynamic GLSM" (DGLSM). Consistency of the model requires the DGLSM to be coupled to additional non-Lagrangian sectors obtained from reduction of the anti-chiral two-form of the 6D theory. These extra sectors include both chiral and anti-chiral currents, as well as spacetime filling non-critical strings of the 6D theory. For each candidate 2d SCFT, we also extract the left- and right-moving central charges in terms of data of the 6D SCFT and the compactification manifold.

P. du Bosque, F. Hassler, D. Lüst, E. Malek: A geometric formulation of exceptional field theory, JHEP 03 (2017), arXiv:1605.00385, abstract, Citations: 11

We formulate the full bosonic SL(5) exceptional field theory in a coordinate-invariant manner. Thereby we interpret the 10-dimensional extended space as a manifold with SL(5)×R+\mathrm{SL}(5)\times\mathbb{R}^+-structure. We show that the algebra of generalised diffeomorphisms closes subject to a set of closure constraints which are reminiscent of the quadratic and linear constraints of maximal seven-dimensional gauged supergravities, as well as the section condition. We construct an action for the full bosonic SL(5) exceptional field theory, even when the SL(5)×R+\mathrm{SL}(5)\times\mathbb{R}^+-structure is not locally flat.

F. Apruzzi, F. Hassler, J. J. Heckman, I. V. Melnikov: UV Completions for Non-Critical Strings, JHEP 07 (2016), arXiv:1602.04221, abstract, Citations: 39

Compactifications of the physical superstring to two dimensions provide a general template for realizing 2D conformal field theories coupled to worldsheet gravity, i.e. non-critical string theories. Motivated by this observation, in this paper we determine the quasi-topological 8D theory which governs the vacua of 2D N = (0,2) gauged linear sigma models (GLSMs) obtained from compactifications of type I and heterotic strings on a Calabi-Yau fourfold. We also determine the quasi-topological 6D theory governing the 2D vacua of intersecting 7-branes in compactifications of F-theory on an elliptically fibered Calabi-Yau fivefold, where matter fields and interaction terms localize on lower-dimensional subspaces, i.e. defect operators. To cancel anomalies / cancel tadpoles, these GLSMs must couple to additional chiral sectors, which in some cases do not admit a known description in terms of a UV GLSM. Additionally, we find that constructing an anomaly free spectrum can sometimes break supersymmetry due to spacetime filling anti-branes. We also study various canonical examples such as the standard embedding of heterotic strings on a Calabi-Yau fourfold and F-theoretic "rigid clusters" with no local deformation moduli of the elliptic fibration.

P. d. Bosque, F. Hassler, D. Lüst: Flux Formulation of DFT on Group Manifolds and Generalized Scherk-Schwarz Compactifications, JHEP 02 (2016), arXiv:1509.04176, abstract, Citations: 24

A flux formulation of Double Field Theory on group manifold is derived and applied to study generalized Scherk-Schwarz compactifications, which give rise to a bosonic subsector of half-maximal, electrically gauged supergravities. In contrast to the flux formulation of original DFT, the covariant fluxes split into a fluctuation and a background part. The latter is connected to a 2D2D-dimensional, pseudo Riemannian manifold, which is isomorphic to a Lie group embedded into O(D,DD,D). All fields and parameters of generalized diffeomorphisms are supported on this manifold, whose metric is spanned by the background vielbein EAIE_A{}^I \in GL(2D2D). This vielbein takes the role of the twist in conventional generalized Scherk-Schwarz compactifications. By doing so, it solves the long standing problem of constructing an appropriate twist for each solution of the embedding tensor. Using the geometric structure, absent in original DFT, EAIE_A{}^I is identified with the left invariant Maurer-Cartan form on the group manifold, in the same way as it is done in geometric Scherk-Schwarz reductions. We show in detail how the Maurer-Cartan form for semisimple and solvable Lie groups is constructed starting from the Lie algebra. For all compact embeddings in O(3,33,3), we calculate EAIE_A{}^I.

R. Blumenhagen, P. du Bosque, F. Hassler, D. Lüst: Generalized Metric Formulation of Double Field Theory on Group Manifolds, JHEP 08 (2015), arXiv:1502.02428, abstract, Citations: 60

We rewrite the recently derived cubic action of Double Field Theory on group manifolds [arXiv:1410.6374] in terms of a generalized metric and extrapolate it to all orders in the fields. For the resulting action, we derive the field equations and state them in terms of a generalized curvature scalar and a generalized Ricci tensor. Compared to the generalized metric formulation of DFT derived from tori, all these quantities receive additional contributions related to the non-trivial background. It is shown that the action is invariant under its generalized diffeomorphisms and 2D-diffeomorphisms. Imposing additional constraints relating the background and fluctuations around it, the precise relation between the proposed generalized metric formulation of DFTWZW{}_\mathrm{WZW} and of original DFT from tori is clarified. Furthermore we show how to relate DFTWZW{}_\mathrm{WZW} of the WZW background with the flux formulation of original DFT.

R. Blumenhagen, F. Hassler, D. Lüst: Double Field Theory on Group Manifolds, JHEP 02 (2015), arXiv:1410.6374, abstract, Citations: 84

A new version of double field theory (DFT) is derived for the exactly solvable background of an in general left-right asymmetric WZW model in the large level limit. This generalizes the original DFT that was derived via expanding closed string field theory on a torus up to cubic order. The action and gauge transformations are derived for fluctuations around the generalized group manifold background up to cubic order, revealing the appearance of a generalized Lie derivative and a corresponding C-bracket upon invoking a new version of the strong constraint. In all these quantities a background dependent covariant derivative appears reducing to the partial derivative for a toroidal background. This approach sheds some new light on the conceptual status of DFT, its background (in-)dependence and the up-lift of non-geometric Scherk-Schwarz reductions.

F. Hassler, D. Lüst, S. Massai: On Inflation and de Sitter in Non-Geometric String Backgrounds, Fortsch. Phys. 65 (2017), arXiv:1405.2325, abstract, Citations: 58

We study the problem of obtaining de Sitter and inflationary vacua from dimensional reduction of double field theory (DFT) on nongeometric string backgrounds. In this context, we consider a new class of effective potentials that admit Minkowski and de Sitter minima. We then construct a simple model of chaotic inflation arising from T-fold backgrounds and we discuss the possibility of trans-Planckian field range from nongeometric monodromies as well as the conditions required to get slow roll.

F. Hassler, D. Lüst: Consistent Compactification of Double Field Theory on Non-geometric Flux Backgrounds, JHEP 1405 (2014), arXiv:1401.5068, abstract, Citations: 47

In this paper, we construct non-trivial solutions to the 2D2D-dimensional field equations of Double Field Theory (DFT) by using a consistent Scherk-Schwarz ansatz. The ansatz identifies 2(Dd)2(D-d) internal directions with a twist UMNU^M{}_N which is directly connected to the covariant fluxes FABC\mathcal{F}_{ABC}. It exhibits 2(Dd)2(D-d) linear independent generalized Killing vectors KIJK_I{}^J and gives rise to a gauged supergravity in dd dimensions. We analyze the covariant fluxes and the corresponding gauged supergravity with a Minkowski vacuum. We calculate fluctuations around such vacua and show how they gives rise to massive scalars field and vectors field with a non-abelian gauge algebra. Because DFT is a background independent theory, these fields should directly correspond the string excitations in the corresponding background. For (Dd)=3(D-d)=3 we perform a complete scan of all allowed covariant fluxes and find two different kinds of backgrounds: the single and the double elliptic case. The later is not T-dual to a geometric background and cannot be transformed to a geometric setting by a field redefinition either. While this background fulfills the strong constraint, it is still consistent with the Killing vectors depending on the coordinates and the winding coordinates, thereby giving a non-geometric patching. This background can therefore not be described in Supergravity or Generalized Geometry.

R. Blumenhagen, M. Fuchs, F. Hassler, D. Lüst, R. Sun: Non-associative Deformations of Geometry in Double Field Theory, JHEP 1404 (2014), arXiv:1312.0719, abstract, Citations: 67

Non-geometric string backgrounds were proposed to be related to a non-associative deformation of the space-time geometry. In the flux formulation of double field theory (DFT), the structure of mathematically possible non-associative deformations is analyzed in detail. It is argued that on-shell there should not be any violation of associativity in the effective DFT action. For imposing either the strong or the weaker closure constraint we discuss two possible non-associative deformations of DFT featuring two different ways how on-shell associativity can still be kept.

F. Hassler, D. Lüst: Non-commutative/non-associative IIA (IIB) Q- and R-branes and their intersections, JHEP 1307 (2013), arXiv:1303.1413, abstract, Citations: 78

In this paper we discuss the construction of non-geometric Q- and R-branes as sources of non-geometric Q- and R-fluxes in string compactifications. The non-geometric Q-branes, being obtained via T-duality from the NS 5-brane or respectively from the KK-monopole, are still local solutions of the standard NS action, where however the background fields G and B possess non-geometric global monodromy properties. We show that using double field theory, redefined background fields tilde G and beta as well as their corresponding effective action, the Q-branes are locally and globally well behaved solutions. Furthermore the R-brane solution can be at least formally constructed using dual coordinates. We derive the associated non-geometric Q- and R-fluxes and discuss that closed strings moving in the space transversal to the world-volumes of the non-geometric branes see a non-commutative or a non-associative geometry. n the second part of the paper we construct intersecting Q- and R-brane configurations as completely supersymmetric solutions of type IIA/B supergravity with certain SU(3) x SU(3) group structures. In the near horizon limit the intersecting brane configurations lead to type II backgrounds of the form AdS4 x M6, where the six-dimensional compact space M6 is a torus fibration with various non-geometric Q- and R-fluxes in the compact directions. It exhibits an interesting non-commutative and non-associate geometric structure. Furthermore we also determine some of the effective four-dimensional superpotentials originating from the non-geometric fluxes.

F. Hassler, F. Ellinger, U. Jörges, R. Wolf, B. Lindner: A high-speed buck converter for efficiency enhancement of W-CDMA power amplifiers, IJWMT 4 (2012), abstract

We present a design strategy for a buck converter, which fulfills the high dynamic requirements of efficient envelope amplifier needed by modern efficiency enhancement techniques for power amplifiers. The proposed DC–DC converter has an innovative control system, which makes it fast, robust, and resource saving. A mathematical model describes its dynamic behavior and is used to find a setup, which gives an optimal compromise between the dynamic performance and efficiency. The approach is applicable to various state-of-the-art communication standards. As an example, an envelope following (EF) power amplifier (PA) for the wideband code-division-multiple-access (W-CDMA) modulation scheme is treated. The corresponding buck converter is implemented in a monolithic chip (except the inductor and the capacitor of the output filter). The measurements with an industry standard W-CDMA PA (RMPA2265) match very well with the forecast of the model and confirm doubling of the average efficiency.


S. Demulder, F. Hassler, D. C. Thompson: An invitation to Poisson-Lie T-duality in Double Field Theory and its applications, PoS CORFU2018 (2019), arXiv:1904.09992, abstract, Citations: 22

Poisson-Lie (PL) T-duality has received much attention over the last five years in connection with integrable string worldsheet theories. At the level of the worldsheet, the algebraic structure underpinning these connections is made manifest with the E\mathcal{E}-model, a first order Hamiltonian description of the string. The E\mathcal{E}-model shares many similarities with Double Field Theory (DFT). We report on recent progress in establishing a precise linkage with DFT as the target space description of the E\mathcal{E}-model. There are three important outcomes of this endeavor:

  1. PL symmetry is made manifest at the level of (generalized) supergravity in DFT.
  2. PL symmetric target spaces are described by a set of generalized frame fields that encode consistent truncations of supergravity.
  3. PL dualisation rules are made explicit and are readily extended to include the R/R sector of the type II theory.
These general results are put into context with their application to the the integrable Yang-Baxter model ($\eta$-deformation). This extended proceedings provides some introductory review of PL and an orientation to the results of arXiv:1707.08624 and arXiv:1810.11446.

R. Blumenhagen, P. du Bosque, F. Hassler, D. Lüst: Double Field Theory on Group Manifolds in a Nutshell, PoS CORFU2016 (2017), arXiv:1703.07347, abstract, Citations: 5

We give a brief overview of the current status of Double Field Theory on Group Manifolds (DFTWZW{}_{\mathrm{WZW}}). Therefore, we start by reviewing some basic notions known from Double Field Theory (DFT) and show how they extend/generalize into the framework of Double Field Theory on Group Manifolds. In this context, we discuss the relationship between both theories and the transition from DFTWZW{}_{\mathrm{WZW}} to DFT. Furthermore, we address some open questions and present an outlook into our current research.

F. Hassler, F. Ellinger, J. Carls: Analysis of buck-converters for efficiency enhancements in power amplifiers for wireless communication, SBMO/IEEE MTT-S IMOC (2007), abstract

An analysis procedure is presented allowing the systematic optimisation of buck-converters, which are required for the efficiency enhancement of power amplifiers in back off mode. All relevant parasitics are included. Based on this model the performance of the envelope following and tracking approaches are investigated for common communication standards such as GSM, UMTS and WLAN. Efficiency enhancements of above 100% are shown.


F. Hassler: Double Field Theory on Group Manifolds (Thesis), preprint July 2015, arXiv:1509.07153, abstract, Citations: 5

This thesis deals with Double Field Theory (DFT), an effective field theory capturing the low energy dynamics of closed strings on a torus. It renders T-duality on a torus manifest by adding DD winding coordinates in addition to the DD space time coordinates. An essential consistency constraint of the theory, the strong constraint, only allows for field configurations which depend on half of the coordinates of the arising doubled space. I derive DFTWZW{}_\mathrm{WZW}, a generalization of the current formalism. It captures the low energy dynamics of a closed bosonic string propagating on a compact group manifold. Its classical action and the corresponding gauge transformations arise from Closed String Field Theory up to cubic order in the massless fields. These results are rewritten in terms of a generalized metric and extended to all orders in the fields. There is an explicit distinction between background and fluctuations. For the gauge algebra to close, the latter have to fulfill a modified strong constraint, while for the former the weaker closure constraint is sufficient. Besides the generalized diffeomorphism invariance known from the original formulation, DFTWZW{}_\mathrm{WZW} is invariant under standard diffeomorphisms of the doubled space. They are broken by imposing the totally optional extended strong constraint. In doing so, the original formulation is restored. A flux formulation for the new theory is derived and its connection to generalized Scherk-Schwarz compactifications is discussed. Further, a possible tree-level uplift of a genuinely non-geometric background (not T-dual to any geometric configuration) is presented. Finally, a long standing problem, the missing of a prescription to construct the twist in generalized Scherk-Schwarz compactifications, is solved. Altogether, a more general picture of DFT and the structures it is based on emerges.

F. Hassler: Semiclassical description of the statistical physics of periodically driven systems, preprint March 2012, abstract

In this thesis time-periodic quantum systems, which are weakly coupled to a heat bath, are explored. Their asymptotic time evolution tt \rightarrow \infty is governed by a quasi equilibrium, where the Floquet states are populated with the probabilities pip_i. In contrast to time-independent systems their occupation probabilities are not equivalent to the Boltzmann distribution but are given by a rate equation, which is based on the transition rates RijR_{ij} between the Floquet states. The transition rates depend on the matrix elements of the coupling operator between the system and the heat bath. In this thesis, these transition rates are calculated by means of the semiclassical WKB-approximation and the EBK-quantisation. To this end, the concept of the extended phase space and the stationary phase approximation is used. The result is an expression for the semiclassical transition rates RijskR^{\mathrm{sk}}_{ij}, which only depends on the classical time evolution of the coupling operator and the winding number of the corresponding cylinder to which the classical motion is bound. In general, this expression is easier to evaluate than its quantum mechanical counterpart. Furthermore, it presents a intuitive interpretation of the transition process between Floquet states in the quasi equilibrium. The accuracy of the demonstrated semiclassical approximation for the transition rates and derived quantities like the effective inverse temperature is shown by comparison with quantum mechanical calculations for various generic examples.

F. Hassler: Design of a DC-DC converter to enhance the efficiency of a UMTS power amplifier, preprint January 2010

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