Topological interfaces in Chern-Simons theory and $AdS_3/CFT_2$

TL;DR

This paper explores the relationship between topological interfaces in 3D Chern-Simons theories and their dual 2D CFTs within the AdS3/CFT2 correspondence, establishing connections and boundary conditions that preserve topological features.

Contribution

It demonstrates how bulk topological interfaces in Chern-Simons theories correspond to boundary interfaces in the dual CFT and identifies boundary counter terms for conserved currents.

Findings

Bulk interfaces map to boundary interfaces in CFT

Boundary counter terms yield conserved currents

Topological features are preserved across the duality

Abstract

Recently, topological interfaces between three-dimensional abelian Chern-Simons theories were constructed. In this note we investigate such topological interfaces in the context of the $AdS_3/CFT_2$ correspondence. We show that it is possible to connect the topological interfaces in the bulk Chern-Simons theory to topological interfaces in the dual CFT on the boundary. In addition for $[U(1)]^{2N}$ Chern-Simons theory on $AdS_3$, we show that it is possible to find boundary counter terms which lead to the $N$ conserved currents in the dual two-dimensional CFT.