Maths HEP Lunchtime Seminars: Aspects of the Chern-Simons/CFT_2 correspondence
11 December 2015 13:00 in CM221
The AdS_3/CFT_2 correspondence asserts that two-dimensional Conformal Field Theories are dual to three-dimensional Einstein gravity with anti-de Sitter boundary conditions. The latter can be formulated as a Chern-Simons theory based on two copies of the sl(2) algebra, and various questions about the universal behavior of 2d CFTs at large central charge may then be addressed in classical Chern-Simons theory. We discuss generalizations of this correspondence in which the bulk Chern-Simons theory is based on a larger gauge algebra: via holography, such theories are dual to 2d CFTs with additional conserved currents beyond the stress tensor, which extend the Virasoro symmetries to e.g. W-algebras. In particular, we describe how to exploit the topological formulation of the 3d bulk theory in order to efficiently compute relevant CFT quantities in the presence of these extended symmetries. Such quantities include partition functions and other thermodynamic potentials, BPS bounds (in supersymmetric setups), and even non-local quantum order parameters such as entanglement and Rényi entropies.