Title: Boundaries, Braneworlds, and Black Holes: Applications of the AdS/BCFT Correspondence

Abstract: The AdS/CFT correspondence is a far-reaching equivalence between theories of quantum gravity in spacetimes with negative cosmological constant, such as anti-de Sitter (AdS) space, and lower-dimensional, non-gravitational quantum systems, such as conformal field theories (CFTs). In this thesis, we will use a version of AdS/CFT applicable to boundary conformal field theories (BCFTs) to investigate the physics of supersymmetric gauge theories, and to develop holographic models for cosmology and black hole physics. We make frequent use of an ansatz for holographic BCFT wherein AdS spacetime ends on a surface called an end-of-the-world (ETW) brane, and of the Ryu-Takayanagi (RT) formula for holographic entanglement entropy. We first study the $U(N)$ $\mathcal{N} = 4$ supersymmetric Yang-Mills (SYM) theory on a half space, with boundary conditions preserving scale invariance and half of the original supersymmetry. We calculate a conjectured RG-monotone called boundary $F$ for the most general such boundary conditions using the RT formula. In some cases, we perform an exact calculation using supersymmetric localization, and find exact agreement for the leading large $N$ term as a function of the ’t Hooft coupling $\lambda$. Next, we introduce a toy model for cosmological physics in the framework of AdS/CFT, wherein a 4D cosmology resides on an ETW brane propagating behind the horizon in a black hole microstate. We study the time-dependent physics of the behind-the-horizon region in such microstates, finding that it can often be probed by the time-dependence of entanglement entropy for sufficiently large CFT subsystems. We investigate the plausibility of obtaining localized 4D gravity on the ETW brane in both effective and microscopic versions of this model.

Last, we consider a doubly-holographic model of a radiating black hole, and apply the RT formula to analyze the time-dependence of the fine-grained entropy of its radiation. We obtain an analogue of the Page curve consistent with unitarity due to a phase transition between RT surfaces, after which the radiation system encodes part of the black hole interior.