This week

We will discuss how to bootstrap string theory in AdS, using N=4 SYM as a concrete example. The first lecture will review the basic ingredients of AdS/CFT: the definitions of AdS and CFT, the correspondence between Kaluza–Klein modes and single-trace operators, and the relation between string scattering in AdS and correlation functions of Kaluza–Klein modes in the CFT. The second lecture will focus on the stress-tensor multiplet four-point function, including its conformal block expansion, the constraints imposed by superconformal Ward identities, and its formulation in Mellin space. The third lecture will introduce the flat-space limit, explain how it acts on the conformal block expansion, and discuss the spectrum of single-trace operators that survives at strong coupling. In the final lecture, we will go beyond the flat-space limit and study the first AdS correction. We will introduce a worldsheet ansatz for this correction and show how matching it to the conformal block expansion fixes the correction completely.

I explain how to take a well-defined flat-space limit of brane models of AdS coupled to a non-gravitating bath. In the dual BCFT this amounts to a triple-scaling limit where both the number of boundary degrees of freedom and the boundary coupling are taken to infinity while the BCFT boundary piecewise approaches a lightcone. This procedure acts on the conformal generators as a Wigner-İnönü contraction, reducing the global BCFT symmetry algebra to the global symmetry algebra of flat space.
I will discuss two natural notions of entanglement entropy of the flat-space dual. These are distinguished by whether modes that have left through future null infinity are included or not and give rise to a vanishing and non-trivial Page curve, respectively. Taking the flat-space limit of topological black holes, the Page time remains finite in two-dimensions. In d > 2 the Page time diverges in the flat limit, since AdS topological black holes become flat-space Rindler horizons.