Higher genus correlators for tensionless $\rm{AdS}_3$ strings

TL;DR

This paper extends the analysis of tensionless AdS3 string correlators from tree-level to higher genus worldsheets, providing evidence for the AdS/CFT correspondence at all orders in perturbation theory.

Contribution

It generalizes the previous tree-level results to higher genus, showing the correlation functions' structure persists beyond leading order in tensionless AdS3 string theory.

Findings

Correlation functions match symmetric orbifold CFT at higher genus.

Correlation functions localize to specific points in moduli space.

Supports the validity of AdS/CFT correspondence at all perturbative orders.

Abstract

It was recently shown in arXiv:2009.11306 that tree-level correlation functions in tensionless string theory on $\rm{AdS}_3\times\rm{S}^3\times\mathbb{T}^4$ match the expected form of correlation functions in the symmetric orbifold CFT on $\mathbb{T}^4$ in the large $N$ limit. This analysis utilized the free-field realization of the $\mathfrak{psu}(1,1|2)_1$ Wess-Zumino-Witten model, along with a surprising identity directly relating these correlation functions to a branched covering of the boundary of $\rm{AdS}_3$. In particular, this identity implied the unusual feature that the string theory correlators localize to points in the moduli space for which the worldsheet covers the boundary of $\rm{AdS}_3$ with specified branching near the insertion points. In this work we generalize this analysis past the tree-level approximation, demonstrating its validity to higher genus worldsheets, and in turn providing strong evidence for this incarnation of the $\rm{AdS}/\rm{CFT}$ correspondence at all orders in perturbation theory.