Vertex Operators in $AdS_3\times S^3$ Background with NS_NS Flux using Berkovits-Vafa-Witten Variables

TL;DR

This paper derives string vertex operators for type IIB theory in an $AdS_3\times S^3$ background with NS-NS flux using Berkovits-Vafa-Witten formalism, connecting supergravity equations and previous vertex operator constructions.

Contribution

It provides explicit calculations of vertex operators in this background and relates them to known supergravity and earlier vertex operator frameworks.

Findings

Recovered linearized supergravity equations from vertex operators

Identified massless modes surviving Kaluza-Klein compactification

Connected new vertex operators to those by Giveon, Kutasov, and Seiberg

Abstract

String equations for the vertex operators of type IIB on $AdS_3\times S^3$ background with NS-NS flux are calculated using Berkovits-Vafa-Witten formalism. With suitable field definitions, the linearized field equations for six-dimensional supergravity and a tensor multiplet on $AdS_3\times S^3$ are recovered from these. We also discuss the massless degrees of freedom that survive the $S^3$ Kaluza-Klein compactification and how our vertex operators are related to the vertex operators introduced by Giveon, Kutasov and Seiberg.