Lobachevsky holography in conformal Chern-Simons gravity

TL;DR

This paper introduces Lobachevsky boundary conditions in conformal Chern-Simons gravity, revealing an asymptotic symmetry algebra with a Virasoro and affine u(1), and explores their implications for non-perturbative states and quantum partition functions.

Contribution

It proposes new boundary conditions leading to specific asymptotic symmetries in conformal Chern-Simons gravity and analyzes their physical and quantum properties.

Findings

Asymptotic symmetry algebra includes Virasoro and u(1)

No black hole solutions found among non-perturbative states

One-loop partition function is ill-defined due to degeneracy

Abstract

We propose Lobachevsky boundary conditions that lead to asymptotically H^2xR solutions. As an example we check their consistency in conformal Chern-Simons gravity. The canonical charges are quadratic in the fields, but nonetheless integrable, conserved and finite. The asymptotic symmetry algebra consists of one copy of the Virasoro algebra with central charge c=24k, where k is the Chern-Simons level, and an affine u(1). We find also regular non-perturbative states and show that none of them corresponds to black hole solutions. We attempt to calculate the one-loop partition function, find a remarkable separation between bulk and boundary modes, but conclude that the one-loop partition function is ill-defined due to an infinite degeneracy. We comment on the most likely resolution of this degeneracy.