Locality and anomalies in warped conformal field theory

TL;DR

This paper explores the properties of warped conformal field theories (WCFTs), introduces new Lagrangian models, analyzes anomalies and hydrostatics, and discusses holographic and gravitational aspects including instabilities and geometric limits.

Contribution

It presents new Lagrangian WCFTs, clarifies their locality conditions, derives anomalies and the warped Cardy formula, and examines holographic and gravitational features of WCFTs.

Findings

All known Lagrangian WCFTs are only local after infinite tuning.

Derived the anomalies and related them to central charges.

Identified instabilities in matter fields in WAdS$_3$ black hole geometries.

Abstract

We study various aspects of warped conformal field theories (WCFTs) in two dimensions. We find new Lagrangian WCFTs, and show that all known Lagrangian WCFTs are local only after an infinite tuning. We deduce the anomalies of WCFTs and relate them to central charges, as well as analyze WCFT hydrostatics, thereby re-deriving the warped analogue of the Cardy formula. Finally, we point out that holographic WCFTs are semi-local, that matter fields in spacelike WAdS$_3$ black hole geometries exhibit a Gregory-Laflamme-like instability, and that WAdS$_3$ throats do not admit a decoupling limit.