Warped Conformal Field Theory as Lower Spin Gravity

TL;DR

This paper explores Warped Conformal Field Theories (WCFTs), revealing their boost symmetry, coupling to a novel warped geometry, and proposing a lower spin gravity dual involving SL(2,R) x U(1) Chern-Simons theory, advancing holography in non-AdS spaces.

Contribution

It introduces warped geometry as a background for WCFTs, identifies their symmetry structure, and proposes a lower spin gravity dual, expanding holographic understanding beyond AdS spaces.

Findings

WCFTs possess a boost symmetry.

Coupling of WCFTs to warped geometry is established.

A lower spin gravity dual via SL(2,R) x U(1) Chern-Simons theory is proposed.

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.