Gravity/CFT correspondence for three dimensional Einstein gravity with a conformal scalar field

TL;DR

This paper explores the gravity/CFT correspondence in three-dimensional Einstein gravity coupled to a conformal scalar field, revealing solutions with infinite central charge and connections to known black hole solutions.

Contribution

It introduces solutions with constant scalar fields and infinite central charge, extending the understanding of holography in scalar-coupled gravity models.

Findings

Solutions with vanishing scalar curvature and asymptotic Virasoro symmetries.

Identification of a family of Schwarzschild solutions conformally related to known black holes.

Evidence of an infinite central charge in the dual CFT.

Abstract

We study the three dimensional Einstein gravity conformally coupled to a scalar field. Solutions of this theory are geometries with vanishing scalar curvature. We consider solutions with a constant scalar field which corresponds to an infinite Newton's constant. There is a class of solutions with possible curvature singularities which asymptotic symmetries are given by two copies of the Virasoro algebra. We argue that the central charge of the corresponding CFT is infinite. Furthermore, we construct a family of Schwarzschild solutions which can be conformally mapped to the Martinez-Zanelli solution of Einstein's equations with a negative cosmological constant coupled to conformal scalar field.