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Wakeham, David

University of British Columbia

The AdS/CFT dictionary connects bulk gravitational physics in an asymptotically anti-de Sitter (AdS) background to the quantum dynamics of a conformally invariant field theory (CFT), defined on the asymptotic boundary. In this thesis, we explore, extend and apply this dictionary for a boundary CFT (BCFT), with a particular focus on the physics of black holes. In a BCFT, a physical boundary is added to the CFT. The simplest dual geometry is an asymptotically AdS spacetime cut off by a physical surface called an end-of-the-world (ETW) brane, homologous to the BCFT boundary. For certain highly symmetric configurations of the BCFT called boundary states, symmetry constrains these ETW branes to a one-parameter family labelled by extrinsic curvature. By placing the CFT boundary in Euclidean time, we construct a one-parameter family of black hole microstates in arbitrary dimension. In two dimensions, we analytically calculate minimal surfaces in the bulk geometry and show that, for some parameter regimes, they pierce the black hole horizon and become disconnected. According to the Hubeny-Rangamani-Ryu-Takayanagi (HRT) formula, these surfaces compute entanglement entropy in the field theory. We find a set of conditions which ensure that the microscopic entanglement entropy, arising from a correlator of twist operators, agrees with the bulk result. In particular, the BCFT reproduces the phase transition between connected and disconnected minimal surfaces. This twist correlator can be immediately evaluated on any conformally related background, giving access to entanglement entropy in a number of other contexts of physical interest. By analytically continuing the thermofield state of a half-line, we arrive at a simple toy model of an evaporating black hole, where the phase transition in minimal surface corresponds to information escaping from the interior. For the BCFT on an interval, this transition can be recast in terms of the performability of a certain set of quantum tasks. We use related techniques to constrain the operator content of BCFTs dual to spacetimes with a sharp brane in arbitrary dimension. We discover they are finely tuned, with a fragile causal structure which becomes “fuzzy” under small changes to the spectrum.

Text

2022-08-12

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/82348

Physics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/