## Gauge/Gravity Duality

USOSIn this course, we will explore the holographic principle, stating that a volume of space can be equivalently described by its lower-dimensional boundary. One might think of a hologram which captures a three-dimensional object on a two-dimensional surface. A particular well studied realization of this idea is the AdS/CFT correspondence which conjectures the equivalence between quantum gravity in Anti-de Sitter (AdS) space and a conformal field theory (CFT) on its boundary. This conjecture is very hard to prove because when one of the two theories is weakly coupled, allowing to use perturbation theory to study it, the other one is strongly coupled - making it very hard to analyse. Despite still being a conjecture, this idea had a huge impact on high-energy physics with an extremely broad range of applications. Latter range from new insights into strongly coupled quantum field theory, required for example to study extreme states of matter like quark-gluon-plasmas or superconductors, to the analysis of black-hole evaporation, that ultimately requires a handle on quantum gravity. We take this as a motivation to study this duality and its main actors in this course in detail. The lectures are tailored towards master and PhD students who are at least familiar with

- electrodynamics
- special relativity
- quantum mechanics.

Basic knowledge of general relativity and quantum field theory is definitely an advantage, but we review their most salient aspects in case you have not yet attended a specialized course on them yet. We will mostly follow the book

- Martin Ammon, Johanna Erdmenger: Gauge/Gravity Duality,

but you might also want to have a look at

- Lewis Ryder: Introduction to General Relativity
- Michael Peskin, Daniel Schroeder: Quantum Field Theory
- Barton Zwiebach: String Theory

for more details on the main actors of the gauge gravity duality.

We will have 2 hours of lectures and 2 hours of tutorial each week. Exercises will be posted here a week before the tutorial they are discussed in. Please keep in mind that active participation in the tutorials is important to pass the course. M.Sc. Luca Scala will be the assistant for the tutorials. Please fell free to contact him or me if you have any questions.

**Important:** Students will be assigned to exercise problems by the system described here, before the tutorial. Please familiarise yourself with this system and do not forget to indicate your preferences.

Additional material for the individual lectures, including the exercises which we discuss in the tutorials, will appear here in due time.

- Abelian and non-abelian gauge theoriesLecture11.10.2024 14:15Tutorial11.10.2024 16:15, exercise
- A primer on general relativityLecture18.10.2024 14:15Tutorial18.10.2024 16:15, exercise
- Properties of anti-de Sitter spaceLecture25.10.2024 14:15
- Transistion to quantum field theory and generating functionsLecture01.11.2024 15:15
- The Large N limit of SU(N) gauge symmetry and planar diagramsLecture08.11.2024 15:15
- Conformal symmetry and CFTsLecture22.11.2024 15:15
- SupersymmetryLecture29.11.2024 15:15
- A primer on string theory, with open strings and gauge theoryLecture06.12.2024 15:15
- Closed strings and gravityLecture13.12.2024 15:15
- Open string boundary conditions and D-branesLecture20.12.2024 15:15
- Statement of the correspondence and the near horizon limit of D3-branesLecture10.01.2025 15:15
- Supergravity action as geneating function for correlation functionsLecture17.01.2025 15:15
- Test of the correspondence through correlation functions and the conformal anomalyLecture24.01.2025 15:15
- Application: holographic derivation of entanglement entropy from AdS/CFTLecture31.01.2025 15:15