Asymptotic Symmetries of String Theory on AdS3 X S3 with Ramond-Ramond Fluxes

TL;DR

The paper constructs explicit vertex operators for the left and right spacetime superconformal generators of string theory on $AdS_3\times S^3$ with Ramond-Ramond flux, using the worldsheet current algebra of the $PSU(1,1|2)$ sigma-model in the hybrid formalism. By formulating nontrivial diffeomorphisms and bulk-to-boundary propagators via the Lambda framework, it derives the spacetime $R$-current algebra and the Virasoro algebra, showing a central extension $c=6I$ where $I$ is spacetime-independent. The work provides a concrete route to classify the string spectrum in RR backgrounds and connects the boundary conformal data to the Brown-Henneaux central charge in this setup, while clarifying the NS-NS limit. It also outlines extensions to the full $N=4$ algebra and potential generalizations to other AdS backgrounds, highlighting links to holography and black hole entropy counts in D1-D5 systems.

Abstract

String theory on AdS3 space-times with boundary conditions that allow for black hole states has global asymptotic symmetries which include an infinite dimensional conformal algebra. Using the conformal current algebra for sigma-models on PSU(1,1|2), we explicitly construct the R-symmetry and Virasoro charges in the worldsheet theory describing string theory on AdS3 X S3 with Ramond-Ramond fluxes. We also indicate how to construct the full boundary superconformal algebra. The boundary superconformal algebra plays an important role in classifying the full spectrum of string theory on AdS3 with Ramond-Ramond fluxes, and in the microscopic entropy counting in D1-D5 systems.