# The large $N$ limit of OPEs in symmetric orbifold CFTs with $\mathcal{N}=(4,4)$ supersymmetry

## TL;DR

This paper investigates the operator product expansion in symmetric orbifold conformal field theories with $
=4$ supersymmetry, revealing a simplified structure at large N involving specific twist operators and fractional excitations.

## Contribution

It extends previous work to $
=4$ supersymmetric cases, proposing a conjecture about the OPE structure at large N and providing evidence through 4-point function analysis.

## Key findings

- OPE at large N involves only a specific class of twist operators and fractional excitations.
- Coincidence limits of 4-point functions support the conjectured OPE structure.
- Fractional modes of superconformal currents reproduce crossing channels.

## Abstract

We explore the OPE of certain twist operators in symmetric product ($S_N$) orbifold CFTs, extending our previous work arXiv:1804.01562 to the case of $\mathcal{N}=(4,4)$ supersymmetry. We consider a class of twist operators related to the chiral primaries by spectral flow parallel to the twist. We conjecture that at large $N$, the OPE of two such operators contains only fields in this class, along with excitations by fractional modes of the superconformal currents. We provide evidence for this by studying the coincidence limits of two 4-point functions to several non-trivial orders. We show how the fractional excitations of the twist operators in our restricted class fully reproduce the crossing channels appearing in the coincidence limits of the 4-point functions.