Correlation functions for chiral primaries in D=6 Supergravity on $AdS_3 \times S^3$

TL;DR

This paper computes the first nontrivial corrections to the equations of motion for chiral primary fields in six-dimensional supergravity on $AdS_3 imes S^3$, revealing similarities with orbifold conformal field theory results.

Contribution

It introduces a method to compute three-point correlation functions for scalar chiral primaries in supergravity, highlighting their correspondence with orbifold CFT results.

Findings

Computed three-point functions for scalar chiral primaries.

Identified similarities between supergravity and orbifold CFT expressions.

Provided insights into the $AdS_3/CFT_2$ correspondence in six dimensions.

Abstract

Six dimensional supergravities on $ADS_3 \times S^3$ present interest due to the role they play in the $AdS/CFT$ correspondence. The correspondence in this case states the equivalence between supergravity on the given background and a still unknown conformal field theory. The conformal field theory in question is expected to appear by deforming of the free conformal field theory on $S^N(T^4)$ in a way which preserves the superconformal symmetry. The purpose of this paper is to compute the first nontrivial corrections to the equations of motion for the chiral primary fields coming from supergravity. Using the methods already developed which involve nontrivial redefinitions of fields, we compute three-point correlation functions for scalar chiral primaries and notice similarities between their expressions and those obtained in the orbifold conformal field theory.