Lobachevsky holography in conformal Chern-Simons gravity

TL;DR

The paper develops Lobachevsky holography by imposing Lobachevsky boundary conditions that render asymptotically $H^2\times \mathbb{R}$ spacetimes in three-dimensional conformal Chern–Simons gravity. It shows that canonical charges are quadratic in fluctuations yet integrable, finite, and conserved, and derives an asymptotic symmetry algebra consisting of a Virasoro algebra with central charge $c=24k$ and an affine $\hat{u}(1)$ current. It identifies four regular non-perturbative states, none of which are black holes, and performs a one-loop analysis that reveals a clean separation between bulk and boundary modes but an ill-defined partition function due to an infinite degeneracy labeled by a weight $h$, which is expected to be resolved by higher-order interactions. The results point toward a dual warped CFT and open avenues for extending Lobachevsky holography to higher-spin theories and more complex boundary conditions.

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.