# Correlation Functions of Warped CFT

## TL;DR

This paper analyzes correlation functions in warped conformal field theories (WCFTs), deriving their forms, establishing bootstrap equations, and connecting these results to holographic dualities with warped AdS spacetimes.

## Contribution

It provides explicit forms for correlation functions in WCFTs, constructs bootstrap equations based on crossing symmetry, and links these to holographic dualities with warped AdS.

## Key findings

- Two and three point functions are fixed by warped conformal symmetry.
- Four point functions can be expressed via global warped conformal blocks.
- The holographic correspondence with warped AdS is supported by matching bulk and boundary Green's functions.

## 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.