Matching of correlators in AdS_3/CFT_2

TL;DR

This paper resolves discrepancies in three-point correlator computations in AdS_3/CFT_2 by including multi-particle operator mixings, confirming non-renormalization of the chiral ring and aligning string theory, orbifold CFT, and supergravity results.

Contribution

It demonstrates that including multi-particle operator mixings at large N reconciles correlator calculations across different frameworks in AdS_3/CFT_2.

Findings

Exact agreement of correlators in string theory and orbifold CFT

Disagreement with supergravity without operator mixing

Inclusion of multi-particle mixings resolves discrepancies

Abstract

Recently exact agreement has been found between three-point correlators of chiral operators computed in string theory on AdS_3 x S^3 x T^4 with NS-NS flux and those computed in the symmetric orbifold CFT. However, it has also been shown that these correlators disagree with those computed in supergravity, under any identification of single particle operators which respects the symmetries. In this note we resolve this disagreement: the key point is that mixings with multi-particle operators are not suppressed even at large N in extremal correlators. Allowing for such mixings, orbifold/string theory operators and supergravity operators can be matched such that both non-extremal and extremal three point functions agree, giving further evidence for the non-renormalization of the chiral ring.