Schedule and lectures

Schedule (orientative)

Lectures

• Julius Grimminger -  Engineering supersymmetric field theories in string theory
  (coming soon)

• Siyul Lee -  Operators, Index and Black Holes in N =4 Super Yang-Mills
  The central theme of the lectures will be operators in the N=4 Super-Yang-Mills theory; how to count and write. We will kick off with representations of Lie groups, then of superconformal algebras, which provide the basic organising principle for the operators. Particular focus will be on the 4d N=4 algebra. Then we will turn to the index, a crucial tool for counting states/operators in supersymmetric theories. We will discuss how the index is invariant under continuous deformations and discover many versions and examples, such as indices with different amounts of supersymmetry and the topologically twisted index for 3d theories.

The latter part of the lectures will utilise the tools to expose exciting recent progress on black hole microstates. We will learn how indices allowed for successful matching between supersymmetric AdS black hole entropy and counting of its microstates via AdS/CFT correspondence, both in micro-canonical and in grand-canonical pictures. Finally, we will turn to the operators themselves that the index counts, and introduce how some of them are thought to correspond to the black hole microstates, namely the fortuity program.

• Cristoforo Iossa - Holographic correlators and black hole perturbation theory
  (coming soon)

• Alice Lüscher - Equivariant localization in supergravity and holography
  Many physical observables in supergravity, which are important in holography, such as free energies, central charges, and operator dimensions, are given by spacetime integrals. The computation of these observables seemingly relies on solving the supergravity field equations, which is often an intractable task. Equivariant localization offers a powerful alternative: it allows one to evaluate the relevant integrals without needing explicit solutions, with the results depending only on global data.

In these lectures, we will first review some basics of holography and supergravity solutions. Then we will derive and explain the localization theorem, before applying it to study some examples in supergravity. Our main result will be a universal formula for the free energy in N=2 d=4 supergravity and dual three-dimensional field theory on various backgrounds. Finally, if time permits, we will cover other interesting setups.