Holograms of Conformal Chern-Simons Gravity

TL;DR

This paper shows that 3D conformal Chern-Simons gravity admits multiple holographic descriptions determined by boundary conditions on the conformal class and the Weyl factor. By classifying into trivial, fixed, and varying Weyl-factor cases, it derives the corresponding asymptotic symmetry algebras, boundary charges, and CFT data, revealing a rich landscape of dual conformal field theories. In the varying-Weyl-factor case, an affine u(1) current emerges and a Sugawara-shifted Virasoro algebra elevates the right-moving central charge by one, interpreted as the presence of a free chiral boson on the boundary. Across the scenarios, the results connect to scaling limits of topologically massive gravity and highlight non-unitary but structurally rich holographic duals for conformal gravity in three dimensions.

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.