# Stress-Tensor Commutator in CFT near the Lightcone

## TL;DR

This paper explores the algebraic structure of stress-tensor commutators in conformal field theories near the lightcone, revealing a Virasoro-like algebra in higher dimensions under specific conditions.

## Contribution

It demonstrates the emergence of a Virasoro-like algebra from stress-tensor commutators in $d>2$ CFTs near the lightcone, under a particular Schwinger term assumption.

## Key findings

- Virasoro-like structure appears near the lightcone in higher-dimensional CFTs.
- The analysis is based on stress-tensor commutation relations and tracelessness conditions.
- A specific assumption on the Schwinger term is crucial for the algebraic emergence.

## Abstract

Starting with the general stress-tensor commutation relations consistent with the Poincar\'e algebra in local quantum field theory, we impose the tracelessness condition and focus on the dominating contributions in the lightcone limit. It is shown that, under a certain assumption on the Schwinger term, a Virasoro-algebra-like structure emerges near the lightcone in $d>2$ conformal field theories.