Four-point functions with multi-cycle fields in symmetric orbifolds and the D1-D5 CFT

We study Sir-invariant four-point functions with two generic multi-cycle fields and two twist-2 fields, at the free orbifold point of the D1-D5 CFT. We derive the explicit factorization of these functions following from the action of the symmetric group on the composite multi-cycle fields. Apart from non-trivial symmetry factors that we compute, the function with multi-cycle operators is reduced to a sum of connected correlators in which the composite fields have, at most, two cycles. The correlators with two double-cycle and two single-cycle fields give the leading order contribution in the large-N limit. We derive explicit formulas for these functions, encompassing a large class of choices for the single- and the double-cycle fields, including generic Ramond ground states, NS chiral fields and the marginal deformation operator. We are thus able to extract important dynamical information from the short-distance OPEs: conformal dimensions, R-charges and structure constants of families of BPS and non-BPS fields present in the corresponding light-light and heavy-light channels. We also discuss properties of generic multi-cycle Q-point functions in M-N/S-N orbifolds, using a technology due to Pakman, Rastelli and Razamat.

Automated summary

We study the invariant four-point functions with generic multi-cycle fields and twist-2 fields in the D1-D5 CFT at the free orbifold point. By considering the action of the symmetric group, we derive the explicit factorization of these functions and simplify their forms. We also investigate the leading order contribution in the large-N limit by studying the correlators with two double-cycle and two single-cycle fields. Furthermore, we discuss the properties of generic multi-cycle Q-point functions in M-N/S-N orbifolds.