Higher genus correlators for tensionless AdS3 strings
Bob Knighton
Abstract
A bstract It was recently shown in [1] that tree-level correlation functions in tensionless string theory on AdS 3 × S 3 × $$ {\mathbbm{T}}^4 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>T</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:math> match the expected form of correlation functions in the symmetric orbifold CFT on $$ {\mathbbm{T}}^4 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>T</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:math> in the large N limit. This analysis utilized the free-field realization of the $$ \mathfrak{psu}{\left(1,\left.1\right|2\right)}_1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>psu</mml:mi> <mml:msub> <mml:mfenced> <mml:mn>1</mml:mn> <mml:mrow> <mml:mfenced> <mml:mn>1</mml:mn> </mml:mfenced> <mml:mn>2</mml:mn> </mml:mrow> </mml:mfenced> <mml:mn>1</mml:mn> </mml:msub> </mml:math> Wess-Zumino-Witten model, along with a surprising identity directly relating these correlation functions to a branched covering of the boundary of 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 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 AdS / CFT correspondence at all orders in perturbation theory.