Twist-nontwist correlators in M^N/S_N orbifold CFTs

TL;DR

This paper extends the Lunin-Mathur covering space technique to include excitations of twist operators and non-twist sector operators in 2D orbifold CFTs, with applications to D1-D5 CFT.

Contribution

It generalizes the covering space method to account for non-twist excitations and insertions, enhancing the analysis of correlation functions in orbifold CFTs.

Findings

Successfully computed correlators with non-twist excitations

Extended the covering space technique to include non-twist operators

Validated the approach with examples from bosonic and D1-D5 CFTs

Abstract

We consider general 2D orbifold CFTs of the form M^N/S_N, with M a target space manifold and S_N the symmetric group, and generalize the Lunin-Mathur covering space technique in two ways. First, we consider excitations of twist operators by modes of fields that are not twisted by that operator, and show how to account for these excitations when computing correlation functions in the covering space. Second, we consider non-twist sector operators and show how to include the effects of these insertions in the covering space. We work two examples, one using a simple bosonic CFT, and one using the D1-D5 CFT at the orbifold point. We show that the resulting correlators have the correct form for a 2D CFT.