Asymptotic dynamics of three-dimensional gravity

Abstract

These are the lectures notes of the course given at the Eleventh Modave Summer School in Mathematical Physics, 2015, aimed at PhD candidates and junior researchers in theoretical physics. We review in details the result of Coussaert-Henneaux-van Driel showing that the asymptotic dynamics of $(2+1)$- dimensional gravity with negative cosmological constant is described at the classical level by Liouville theory. Boundary conditions implement the asymptotic reduction in two steps: the first set reduces the $SL(2,\mathbb{R})\times SL(2,\mathbb{R})$ Chern-Simons action, equivalent to the Einstein action, to a non-chiral $SL(2,\mathbb{R})$ Wess-Zumino-Witten model, while the second set imposes constraints on the WZW currents that reduce further the action to Liouville theory. We discuss the issues of considering the latter as an effective description of the dual conformal field theory describing AdS${}_3$ gravity beyond the semi-classical regime.

36 pages, 2 figures. Lecture notes prepared for the Eleventh Modave Summer School in Mathematical Physics, September 2015, Belgium

References in corpus (6)

• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Setting the boundary free in AdS/CFT
• Entropy of three-dimensional asymptotically flat cosmological solutions
• Symplectic and Killing Symmetries of AdS${}_3$ Gravity: Holographic vs Boundary Gravitons
• Boundary dynamics of asymptotically flat 3D gravity coupled to higher spin fields

Cited by in corpus (1)

• Most general flat space boundary conditions in three-dimensional Einstein gravity