Locality and anomalies in warped conformal field theory

TL;DR

This work analyzes two-dimensional warped conformal field theories (WCFTs) from several angles: locality, anomalies, thermodynamics, and holography. It shows that Lagrangian WCFTs are local only after an infinite tuning of non-local operators and derives a three-parameter anomaly structure (boost, mixed boost/Weyl, gravitational) that fixes the Virasoro and Kac–Moody central charges, enabling a warped Cardy-style thermodynamics via a plane-to-cylinder map. The hydrostatic analysis yields explicit expressions for the currents and entropy, confirming the warped Cardy formula and clarifying the role of anomaly data in finite-temperature behavior. On the holography side, the putative duals to gravity on spacelike WAdS$_3$ are semi-local and suffer from instabilities and backreaction issues, implying that holographic WCFTs are inherently non-local and do not admit a straightforward locality-based anomaly matching.

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.