Warped Flatland

TL;DR

This paper explores warped flat geometries in three-dimensional topologically massive gravity, analyzing their structure, symmetries, and thermodynamics, and extending the Warped Cardy formula to compute their entropy.

Contribution

It introduces warped flat geometries as quotients of warped flat spacetime, studies their asymptotic symmetries, and generalizes the Warped Cardy formula for entropy calculation.

Findings

Warped flat geometries are quotients of warped flat spacetime.

The asymptotic symmetry group is a Warped CFT algebra with zero current level.

The generalized Warped Cardy formula accurately reproduces the entropy.

Abstract

We study warped flat geometries in three-dimensional topologically massive gravity. They are quotients of global warped flat spacetime, whose isometries are given by the 2-dimensional centrally extended Poincar\'e algebra. The latter can be obtained as a certain scaling limit of Warped AdS3 space with a positive cosmological constant. We discuss the causal structure of the resulting spacetimes using projection diagrams. We study their charges and thermodynamics, together with asymptotic Killing vectors preserving a consistent set of boundary conditions including them. The asymptotic symmetry group is given by a Warped CFT algebra, with a vanishing current level. A generalization of the derivation of the Warped Cardy formula applies in this case, reproducing the entropy of the warped flat cosmological spacetimes.