Hi, I am Falk Hassler, a postdoctoral researcher at the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University.
My life as a postdoc started 2015, when I finished my PhD at the Ludwig Maximlians University in Munich. Since then, its has not been short of adventures. I had the opportunity to work in many exciting places with great people from all over the world: New York City, Chapel Hill (North Carolina), Philadelpha, Ovideo (Spain) and College Station (Texas) have been home to my family (wife Antje and our daugther Amy who was born in Philly) and me. After growing up in a small town in the north of Germany, I would have never dreamed that one day physics leds me to all these incredible places. You can fine more details in my CV.
Imagine, we take a coffee mug and zoom in with a very powerful microscope. Eventually we will discover that the mug is made out of atoms. These atoms have protons and neutron in their core which consists of quarks held together by gluons. We don't have machines yet to zoom in much further. But one things is certain, at the incredible small scale of meters something dramatical has to happen. At this point the two fundamental ingredients of physics, general relativity and quantum field theory, start to contradict each other.
My research takes us exactly to this point. Although we do not have any experimental data at this scale yet, the last 50 years have produced some incredible detailed ideas what we might find. All of them are based on the fundamental mechanisms in physics that we already have confirmed experimentally. The most studied idea is that point particles have to be ultimately be substituted by extended object, strings.
Strings are so fundamental that not only particle are made of them but also the interactions between them and even spacetime itself.
Hence, we face a crucial change of paradigms. Point particles have a natural notion of distance. A simple example is a free particle on a ring. Its energy spectrum is indirect proportional to the radius. Thus, we could easily distinguish between large and small rings. Distance between points is also the defining concept in Riemannian geometry that underpins general relativity.
Things become more subtle if we look at strings because in addition to the center of mass motion of point particles, they can wind around the circle. Hence, their spectrum is characterised by two quantum numbers. Remarkably, it is the same on two circles, one larger and the other one smaller than the length of the string. Just the role of momentum and winding gets flipped. This effect is called T-duality and it obfuscates the clear notion of distance required to define geometry. Therefore strings ultimately require to work with a generalisation of geometry.
My work has reveal how this adapted version of geometry can capture T-dualities which go far beyond the simple example we have just discussed. In contrast to a circle or a torus, the spacetimes I am interested in are curved.
Strings in curved backgrounds automatically induce higher curvature orrections that modify the Einstein-Hilbert action of point particles. These corrections are essential to understand how a quantum theory of gravity might resolve singularities at the center of black holes or the Big Bang. Thus, my currents efforts focus on how T-duality allows to explicitly compute these corrections. Moreover, my work gives a new handle on integrable string models which are an indispensable tool in the long standing quest of proving the AdS/CFT correspondence, perhaps the successful spin-offs of string theory.
By using dualities in string theory, I explore quantum field theory and quantum gravity at strong coupling, very high energies and small distances. My current focus lies on double/exceptional field theory, an effective target space description of string/M-theory, which makes T-/U-duality manifest, and (super)conformal field theories, (S)CFTs, in two and more dimensions. On the formal side, I look into the underlying principles of generalized geometry, non-commutative or even non-associative geometry; especially, how they naturally arise from strings and higher dimensional membranes probing spacetime. String field theory, which allows to extract a lot of amazing mathematical structure from the string's worldsheet CFT, is a powerful tool in this realm. Although this is still a perturbative approach, it can point out underlying symmetry principles which allow to access the non-perturbative regime too. A very prominent example is supersymmetry which intriguingly allows to study certain protected sectors of a theory (like BPS solutions) at strong coupling. These special sectors are also an indispensable tool to study higher dimensional SCFTs which sometimes even do not have a weak coupling limit. Having all these fundamental aspects in mind, I am interested in concrete applications of them, too. They range from flux compactifications, over consistent truncations to simple toy models for inflation in cosmology. Recently, I explored the connection between double field theory and Poisson-Lie T-duality. This is very exciting, because the latter is closely related to integrable deformations of two dimensional -models. Such deformations are extensively studied in connection with the AdS/CFT correspondence. They exhibit the rich mathematical structure of quantum groups.