Three-point functions for M^N/S^N orbifolds with N=4 supersymmetry

TL;DR

The paper computes large-N three-point functions of chiral operators in M^N/S^N orbifold CFTs with N=4 supersymmetry, constructing a universal basis of chiral twists σ_n^± by coupling twist insertions to the N=4 current algebra. By mapping to covering surfaces and incorporating current and spin-field insertions, the authors reduce the SUSY problem to Liouville-type conformal anomaly factors times current-spin correlators on the cover, with explicit free-field realizations enabling exact fusion coefficients. They derive neat closed forms for the holomorphic and antiholomorphic fusion coefficients, including general expressions for arbitrary SU(2) representations, and show that the sphere (genus-0) contribution dominates at large N, with higher-genus corrections suppressed as 1/N^g. The results are universal (M-independent) and provide a clean bridge to AdS3×S3×M holography, offering a baseline for comparisons with dual supergravity and Ramond-sector correlators at the orbifold point.

Abstract

The D1-D5 system is believed to have an `orbifold point' in its moduli space where its low energy theory is a N=4 supersymmetric sigma model with target space M^N/S^N, where M is T^4 or K3. We study correlation functions of chiral operators in CFTs arising from such a theory. We construct a basic class of chiral operators from twist fields of the symmetric group and the generators of the superconformal algebra. We find explicitly the 3-point functions for these chiral fields at large N; these expressions are `universal' in that they are independent of the choice of M. We observe that the result is a significantly simpler expression than the corresponding expression for the bosonic theory based on the same orbifold target space.