$\text{AdS}_3/\text{CFT}_2$ at higher genus

Abstract

We continue our study of the worldsheet theory of superstrings on $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathbb{T}^4$ in the tensionless limit arXiv:1911.00378. We consider the theory on higher genus surfaces. We give evidence that the worldsheet correlators localise on certain worldsheets that cover the boundary of $\mathrm{AdS}_3$ holomorphically. This simplifies the string moduli space integral dramatically to a finite sum. This property shows that the higher genus corrections of the string worldsheet reproduce the structure of the $1/N$ corrections in the dual symmetric orbifold CFT $\mathrm{Sym}^N(\mathbb{T}^4)$.