Duality of the Superstring in Superspace

TL;DR

This paper explores the duality transformations of superstring theory in superspace, deriving dual backgrounds and analyzing cases with constant and superfield-dependent backgrounds, extending previous duality results.

Contribution

It generalizes the first order formalism to superspace, deriving dual backgrounds for superstrings and analyzing cases with constant and superfield-dependent backgrounds.

Findings

Recovered G → G^{-1} duality for zero antisymmetric tensor

Derived explicit duality transformations for superfield-dependent backgrounds

Extended duality analysis to superspace formalism

Abstract

The evolution of a closed NSR string is considered in the background of constant graviton and antisymmetric fields. The $\sigma$-model action is written in a manifestly supersymmetric form in terms of superfields. The first order formalism adopted for the closed bosonic string is generalised to implement duality transformations and the constant dual backgrounds are obtained for the dual theory. We recover the $G \rightarrow G^{-1}$ duality for the case when antisymmetric tensor field is set to zero. Next, the case when the backgrounds depend on one superfield, is also analysed. This scenario is similar to the cosmological case envisaged for the bosonic string. The explicit form of the duality transformation is given for this case.