Attractor Flows from Defect Lines

TL;DR

This paper explores how defect lines in 2D conformal field theories induce flows on moduli spaces, revealing connections to gradient flows of g-functions and attractor flows in supergravity.

Contribution

It introduces a novel approach linking defect-induced Casimir forces to moduli space flows and relates supersymmetric boundary flows to black hole attractor flows.

Findings

Flows are reparametrizations of gradient flows of g-functions.

Supersymmetric boundary flows match attractor flows in N=2 supergravity.

Casimir forces can be used to construct moduli space flows.

Abstract

Deforming a two dimensional conformal field theory on one side of a trivial defect line gives rise to a defect separating the original theory from its deformation. The Casimir force between these defects and other defect lines or boundaries is used to construct flows on bulk moduli spaces of CFTs. It turns out, that these flows are constant reparametrizations of gradient flows of the g-functions of the chosen defect or boundary condition. The special flows associated to supersymmetric boundary conditions in N=(2,2) superconformal field theories agree with the attractor flows studied in the context of black holes in N=2 supergravity.