Warped Conformal Field Theory as Lower Spin Gravity

TL;DR

This work develops a covariant framework for Warped Conformal Field Theories (WCFTs), the simplest non-Lorentz invariant QFTs with a Virasoro–Kac–Moody symmetry, by introducing Warped Geometry and Warped Weyl invariance. It shows how to couple WCFTs to this non-Riemannian background and derives the corresponding conserved currents and Ward identities, including explicit free WCFTs (Warped Weyl spinor and Warped bc system). The authors then construct a minimal holographic dual, called Lower Spin Gravity, described by SL(2)×U(1) Chern-Simons theory, and demonstrate how WCFT symmetries arise as boundary charges, reproducing Warped AdS3 geometries. This framework provides a clean, UV-friendly route to non-AdS holography and a platform for exploring deformations and higher-spin generalizations such as W_N theories.

Abstract

Two dimensional Warped Conformal Field Theories (WCFTs) may represent the simplest examples of field theories without Lorentz invariance that can be described holographically. As such they constitute a natural window into holography in non AdS space-times, including the near horizon geometry of generic extremal black holes. It is shown in this paper that WCFTs posses a type of boost symmetry. Using this insight, we discuss how to couple these theories to background geometry. This geometry is not Riemannian. We call it Warped Geometry and it turns out to be a variant of a Newton-Cartan structure with additional scaling symmetries. With this formalism the equivalent of Weyl invariance in these theories is presented and we write two explicit examples of WCFTs. These are free fermionic theories. Lastly we present a systematic description of the holographic duals of WCFTs. It is argued that the minimal setup is not Einstein gravity but an SL(2,R) x U(1) Chern-Simons Theory, which we call Lower Spin Gravity. This point of view makes manifest the definition of boundary for these non AdS geometries. This case represents the first step towards understanding a fully invariant formalism for W_N field theories and their holographic duals.