The OPE of bare twist operators in bosonic $S_N$ orbifold CFTs at large $N$

TL;DR

This paper investigates the operator product expansions of twist operators in bosonic symmetric orbifold conformal field theories at large N, proposing that only bare twists and their fractional excitations appear in the OPE.

Contribution

It conjectures and provides evidence that at large N, the OPE of bare twist operators includes only bare twists and fractional Virasoro mode excitations, depending solely on twist lengths and central charge.

Findings

Confirmed the structure of twist operator OPEs at large N.

Matched coefficients of four-point functions with fractional Virasoro excitations.

Supported the conjecture with non-leading order calculations.

Abstract

In this work, we explore the twist operator OPEs of a generic bosonic symmetric product ($S_N$) orbifold CFT. We conjecture that at large $N$ the OPE of bare twist operators contains only bare twists and excitations of bare twists with fractional Virasoro modes. These fractionally excited operators are the only ones that depend exclusively on the lengths of the twists and the central charge, agreeing with the general structure of correlators of bare twists found in the literature. To provide evidence for this, we study the coincidence limit of a four point function of bare twist operators to several non-leading orders. We show how the coefficients of these powers can be reproduced by considering bare twist operators excited by fractional Virasoro modes in the exchange channels.