Holograms of Conformal Chern-Simons Gravity

TL;DR

This paper explores various holographic descriptions of conformal Chern-Simons gravity in three dimensions, revealing how boundary conditions and Weyl factors influence the asymptotic symmetry group and dual conformal field theory features.

Contribution

It demonstrates how different boundary conditions and Weyl factors lead to diverse holographic duals, including an affine u(1) algebra and a free chiral boson in the dual CFT.

Findings

Agreement with scaled topologically massive gravity for fixed Weyl factor

Enhanced asymptotic symmetry group with varying Weyl factor

Weyl factor acts as a free chiral boson in the dual CFT

Abstract

We show that conformal Chern-Simons gravity in three dimensions has various holographic descriptions. They depend on the boundary conditions on the conformal equivalence class and the Weyl factor, even when the former is restricted to asymptotic Anti-deSitter behavior. For constant or fixed Weyl factor our results agree with a suitable scaling limit of topologically massive gravity results. For varying Weyl factor we find an enhancement of the asymptotic symmetry group, the details of which depend on certain choices. We focus on a particular example where an affine u(1) algebra related to holomorphic Weyl rescalings shifts one of the central charges by 1. The Weyl factor then behaves as a free chiral boson in the dual conformal field theory.