Correlation Functions of Warped CFT

TL;DR

This work analyzes correlation functions in warped conformal field theories (WCFTs), showing that global warped conformal symmetry fixes two- and three-point functions and constrains four-point functions up to a function of the cross ratio $x$. It introduces a warped conformal bootstrap based on crossing symmetry and demonstrates that, at large central charge, four-point blocks decompose into Virasoro and U(1) components, paralleling holographic expectations with warped AdS. The paper also develops finite-temperature correlators via a warped mapping, derives the Rényi entropy from twist fields including a new parameter $\alpha$, and provides a dictionary to match bulk scattering in WAdS to retarded Green’s functions in WCFT, supporting the WAdS/WCFT holographic correspondence.

Abstract

Warped conformal field theory (WCFT) is a two dimensional quantum field theory whose local symmetry algebra consists of a Virasoro algebra and a U(1) Kac-Moody algebra. In this paper, we study correlation functions for primary operators in WCFT. Similar to conformal symmetry, warped conformal symmetry is very constraining. The form of the two and three point functions are determined by the global warped conformal symmetry while the four point functions can be determined up to an arbitrary function of the cross ratio. The warped conformal bootstrap equation are constructed by formulating the notion of crossing symmetry. In the large central charge limit, four point functions can be decomposed into global warped conformal blocks, which can be solved exactly. Furthermore, we revisit the scattering problem in warped AdS spacetime (WAdS), and give a prescription on how to match the bulk result to a WCFT retarded Green's function. Our result is consistent with the conjectured holographic dualities between WCFT and WAdS.