Hexagonalization in $AdS_3 \times S^3 \times T^4$: Mirror Corrections

TL;DR

This paper advances the hexagonalization framework for $AdS_3 imes S^3 imes T^4$ by computing mirror corrections, enabling the calculation of structure constants for finite bridge lengths and exploring $n$-point functions.

Contribution

It completes the hexagonalization approach by deriving mirror corrections for finite bridge lengths and demonstrates the non-renormalization of half-BPS operators.

Findings

Mirror corrections computed for finite bridge lengths.

Half-BPS operators do not receive mirror corrections.

First steps towards $n$-point function calculations.

Abstract

A big open problem in $AdS_3 \times S^3 \times T^4$ holographic duality is to compute the CFT data of the dual theory. In this direction recently it was introduced the hexagonalization framework in the $AdS_3$ context. It allows the computation of the structure constants of the CFT$_2$ dual in the planar limit non-perturbatively, however in this proposal it was introduced only the asymptotic part of the hexagon valid for correlators with asymptotically large bridge lengths. In this work we complete this picture by computing the so called mirror corrections that allow to describe structure constants for finite bridge lengths and as a byproduct we also prove that the half-BPS operators in the theory do not receive these corrections. We end up by giving the first steps on using hexagonalization to compute $n$-point functions in the $AdS_3 \times S^3 \times T^4$ holographic duality.