Boundary Dynamics of Three-Dimensional Asymptotically Anti-de Sitter Space-Times

TL;DR

This paper explores the boundary dynamics and asymptotic symmetries of three-dimensional anti-de Sitter space-times, linking them to conformal field theories and black hole entropy calculations.

Contribution

It provides a detailed analysis of the boundary conformal field theory and central charge in asymptotically AdS3 space-times, connecting gravitational symmetries to CFT results.

Findings

Calculation of the central charge in asymptotic symmetry algebra.

Derivation of boundary conformal field theory from AdS3.

Reproduction of black hole entropy via Strominger's method.

Abstract

This thesis is organized as follows. In Chapter 2, some preliminaries are given on isometries and conformal symmetries, and we become familiar with the Virasoro algebra. Two examples of classical central charges are discussed. Chapter 3 contains an introduction to the Hamiltonian formulation of gauge theories in the context of Maxwell theory. The knowledge gained in Chapter 3 is applied to general relativity in Chapter 4. The Hamiltonian is shown to acquire a surface term due to the presence of the boundary. The geometrical properties of anti-de Sitter space and the BTZ black hole are the subject of Chapter 5. The main part of the discussion follows in Chapter 6, which contains the calculation of the central charge in the asymptotic symmetry algebra of asymptotically AdS3 space-times. After some preliminaries on the AdS/CFT correspondence and Chern-Simons theory, the derivation of the boundary conformal field theory is summarized in Chapter 7. Finally, Strominger's entropy calculation is presented in Chapter 8, along with some comments on this approach.