Lightcone commutator and stress-tensor exchange in d&gt;2 conformal field theories

Kuo-Wei Huang

doi:10.1103/physrevd.102.021701

Abstract

Motivated by developing a field-theoretic algebraic approach to the universal part of the stress-tensor sector of a scalar four-point function in a class of higher-dimensional CFTs, we construct a mode operator, ${\cal L}_m$, near the lightcone in $d=4$ CFTs and show that it leads to a Virasoro-like commutator, including a regularized central-term. As an example, we describe how to reproduce the $d=4$ single-stress tensor exchange contribution in the lightcone limit by a mode summation. A general-$d$ extension is included. We comment on possible generalizations.

Highlights

The existence of the Virasoro symmetry lies at the heart of two-dimensional conformal field theories
The recent d > 2 results share intriguing similarities with d 1⁄4 2 conformal field theories (CFTs) and we are motivated to search for a Virasoro-like derivation in the lightcone limit in d > 2 CFTs; we largely focus on d 1⁄4 4 in this note
We have described a derivation of the near-lightcone single-stress tensor block in d > 2 CFTs via a Virasoro-like generator

Summary

INTRODUCTION

The existence of the Virasoro symmetry lies at the heart of two-dimensional conformal field theories Such an infinite-dimensional stress-tensor algebra dictates universal behaviors of d 1⁄4 2 systems, allowing computable multipoint correlation functions and critical exponents [1]. The universality, more precisely, means that the operator product expansion (OPE) coefficients of the lowest-twist multistress tensors are protected, in the sense that they are fixed by dimensions of scalars and the central charge CT. Based on the most general stress-tensor commutators consistent with the Poincarealgebra in local QFT [31], it was shown that, under an assumption on the Schwinger term, a Virasoro-like stress-tensor commutator emerges near the lightcone in d 1⁄4 4 CFTs. Here, we would like to start to build a bridge between the stress-tensor commutator and the conformal block decomposition of a scalar four-point function. While the general story is left to future work, we will make some preliminary remarks on a possible multistress tensor generalization

A LIGHTCONE MODE OPERATOR

GENERAL d STRESS-TENSOR EXCHANGE FROM Lm

CONCLUDING REMARKS AND OUTLOOK