# Light cone OPE in a CFT with lowest twist scalar primary

## TL;DR

This paper analyzes the lightcone operator product expansion in conformal field theories with a lowest twist scalar primary, revealing the dominance of stress tensor contributions and the absence of a scalar ANEC analogue.

## Contribution

It provides a detailed study of the lightcone OPE structure in CFTs with a lowest twist scalar, highlighting the roles of stress tensor and scalar operators and the non-existence of a scalar ANEC.

## Key findings

- Stress tensor dominates the leading order in lightcone OPE.
- Scalar operators contribute at subleading order.
- No scalar analogue of the average null energy condition exists.

## Abstract

We study the operator product expansion (OPE) of two identical scalar primary operators in the lightcone limit in a conformal field theory where a scalar is the operator with lowest twist. We see that in CFTs where both the stress tensor and a scalar are the lowest twist operators, the stress tensor contributes at the leading order in the lightcone OPE and the scalar contributes at the subleading order. We also see that there does not exist a scalar analogue of the average null energy condition (ANEC) for a CFT where a scalar is the lowest twist operator.