Bending branes for DCFT in two dimensions

TL;DR

This paper develops a holographic model for defect conformal field theories in two dimensions, analyzing the backreaction of a matter-filled brane in AdS3 and deriving exact solutions relevant for entanglement entropy and Kondo models.

Contribution

It introduces a backreacted holographic dual for 2D DCFTs with exact solutions for branes with matter, linking energy conditions to geometry and entanglement entropy.

Findings

Israel junction conditions relate to energy conditions for brane matter.

Exact solutions for branes with perfect fluid matter, including scalar fields.

Implications for holographic entanglement entropy and Kondo models.

Abstract

We consider a holographic dual model for defect conformal field theories (DCFT) in which we include the backreaction of the defect on the dual geometry. In particular, we consider a dual gravity system in which a two-dimensional hypersurface with matter fields, the brane, is embedded into a three-dimensional asymptotically Anti-de Sitter spacetime. Motivated by recent proposals for holographic duals of boundary conformal field theories (BCFT), we assume the geometry of the brane to be determined by Israel junction conditions. We show that these conditions are intimately related to the energy conditions for the brane matter fields, and explain how these energy conditions constrain the possible geometries. This has implications for the holographic entanglement entropy in particular. Moreover, we give exact analytical solutions for the case where the matter content of the brane is a perfect fluid, which in a particular case corresponds to a free massless scalar field. Finally, we describe how our results may be particularly useful for extending a recent proposal for a holographic Kondo model.