Matching of correlators in AdS_3/CFT_2

TL;DR

This work resolves a prior mismatch between supergravity and string/orbifold CFT three-point functions for chiral primaries in $AdS_3/CFT_2$ by showing that mixings with multi-particle operators are not suppressed at large $N$ in extremal correlators. A symmetry-respecting linear map with a specifically fixed matrix ${\cal M}$ aligns non-extremal correlators across the three frameworks, while extremal correlators necessitate additional non-linear (quadratic) operator mixings to achieve agreement. The results provide strong evidence for a non-renormalization of the chiral ring and clarify how bulk supergravity operators correspond to combinations of string vertex and orbifold CFT operators. The analysis highlights the importance of large-$N$ scaling and operator mixing in AdS/CFT for precise matching across moduli and demonstrates how non-linear mixings reconcile extremal correlators, with potential implications for broader non-renormalization phenomena.

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.