From Symmetric Product CFTs to ${\rm AdS}_3$

TL;DR

This paper explores the connection between symmetric orbifold CFT correlators and string theory on AdS3 by analyzing branched covers via a matrix model, revealing a geometric and analytical structure that elucidates gauge-string duality.

Contribution

It introduces a matrix model approach to describe branched covers in symmetric orbifold CFTs in a large twist limit, linking them to spectral curves and Strebel differentials, thus providing a geometric realization of AdS3/CFT2 duality.

Findings

Branched covers described by a Penner-like matrix model.

Spectral curve related to Strebel quadratic differential.

Correlators expressed as integrals over world-sheet moduli space.

Abstract

Correlators in symmetric orbifold CFTs are given by a finite sum of admissible branched covers of the 2d spacetime. We consider a Gross-Mende like limit where all operators have large twist, and show that the corresponding branched covers can be described via a Penner-like matrix model. The limiting branched covers are given in terms of the spectral curve for this matrix model, which remarkably turns out to be directly related to the Strebel quadratic differential on the covering space. Interpreting the covering space as the world-sheet of the dual string theory, the spacetime CFT correlator thus has the form of an integral over the entire world-sheet moduli space weighted with a Nambu-Goto-like action. Quite strikingly, at leading order this action can also be written as the absolute value of the Schwarzian of the covering map. Given the equivalence of the symmetric product CFT to tensionless string theory on ${\rm AdS}_3$, this provides an explicit realisation of the underlying mechanism of gauge-string duality originally proposed in arXiv:hep-th/0504229 and further refined in arXiv:0803.2681.