Anatoly Dymarsky, "Classical and quantum codes, 2d CFTs and holography"

ITMP seminar, Mar 6, 2024
Speaker: Prof. Anatoly Dymarsky, University of Kentucky
Title: Classical and quantum codes, 2d CFTs and holography
Abstract: There is a rich connection between classical and quantum codes and holographic correspondence connecting 2d CFTs and abelian 3d Chern-Simons theories. In the 3d language the codes emerge as a way to parametrize condensable anyons. Upon condensation 3d topological field theory gives rise to 2d CFT at the boundary. This provides a way to construct 2d CFTs from codes - the so called "code CFTs". This construction has a natural interpretation in terms of a CSS quantum code (defined in terms of the original classical code, defining the CFT). From the holographic point of view a particularly interesting question is that of an ensemble of codes and associated code CFTs. The ensemble of boundary theories is holographically dual to "Chern-Simons gravity", a topological field theory that sums over 3d topologies.