B-RNS-GSS Type II superstring in Ramond-Ramond backgrounds

TL;DR

This paper extends the B-RNS-GSS formalism to describe Type II superstrings in curved backgrounds, expressing the BRST charge via superconformal generators and linking their relations to supergravity equations, with a focus on the integrable AdS5×S5 case.

Contribution

It introduces an extended formalism combining RNS and GS variables for Type II superstrings in curved backgrounds, connecting algebraic relations to supergravity equations.

Findings

BRST charge expressed in superconformal generators

Relations imply Type II supergravity equations

Classical integrability shown for AdS5×S5 background

Abstract

The B-RNS-GSS formalism containing both RNS and GS worldsheet variables is extended for the description of the Type II superstring in curved backgrounds. The BRST charge of the theory is expressed in terms of $N=(1,1)$ superconformal generators $(T,G; {\widehat{T}}, {\widehat{G}})$, and the classical anticommutation relations $\{G,G\}=-2T$ and $\{{\widehat{G}},{\widehat{G}}\}=-2{\widehat{T}}$ are shown to imply the Type II supergravity equations of motion. The particular case of the Type IIB superstring in an $AdS_5\times S^5$ background is discussed and shown to be classically integrable.