Mirror Mirror On The Wall: On 2d Black Holes and Liouville Theory

TL;DR

This paper derives a duality between 2D Euclidean black holes and supersymmetric Liouville theory, realized via domain walls in a 3D gauge theory, revealing new insights into their mirror symmetry and instanton effects.

Contribution

It provides a novel derivation of the duality using domain wall realizations in 3D gauge theories, connecting worldsheet instantons with classical domain wall scattering.

Findings

Duality between 2D black holes and Liouville theory established.

Domain walls in 3D gauge theory realize the dual conformal field theories.

Worldsheet instanton effects are interpreted as classical domain wall scattering.

Abstract

We present a novel derivation of the duality between the two-dimensional Euclidean black hole and supersymmetric Liouville theory. We realise these (1+1)-dimensional conformal field theories on the worldvolume of domain walls in a (2+1)-dimensional gauge theory. We show that there exist two complementary descriptions of the domain wall dynamics, resulting in the two mirror conformal field theories. In particular, effects which are usually attributed to worldsheet instantons are captured by the classical scattering of domain walls.