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

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.

String theory on AdS3 and the symmetric orbifold of Liouville theory

“…(2.34) has exactly the same form as for the case of a symmetric orbifold, where the L n modes act on the covering space, while the L m generators are those of the seed theory, see e.g. [25][26][27]. The analysis for the other DDF operators is similar.…”

Correlators of the symmetric product orbifold

“…where h 0 w is given by (2.20). 13 A similar analysis has been performed in Appendix B of [36] and investigated more in general in [45].…”

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

“…To extend that insight, in [1] the same group of us considered the OPE between two bare twists in a generic bosonic symmetric product (S N ) orbifold CFT. We conjectured that at leading order in 1/N , the only operators that show up in the OPE of two bare twist operators are bare twist operators and their excitations by fractional Virasoro modes.…”