On type II superstrings in bosonic backgrounds: the role of fermions and T-duality

TL;DR

This paper derives second-order fermionic actions for type II superstrings in general bosonic backgrounds, highlighting the role of T-duality and supersymmetry, and presents simplified, elegant formulations.

Contribution

It provides a systematic derivation of type II superstring actions up to second order in fermions, incorporating T-duality and background supersymmetry considerations.

Findings

Actions are $mbda$-symmetric and supersymmetric in backgrounds with preserved supersymmetry.

Type IIa action obtained from 11D supermembrane via double dimensional reduction.

Type IIb action derived through a generalized T-duality, resulting in simplified expressions.

Abstract

We derive the actions for type II Green-Schwarz strings up to second order in the fermions, for general bosonic backgrounds. We base our work on the so-called normal coordinate expansion. The resulting actions are $\kappa$-symmetric and, for the case of surviving background supersymmetries, supersymmetric. We first obtain the type IIa superstring action from the 11D supermembrane by double dimensional reduction. Then, by means of a generalization of T-duality we derive the type IIb superstring action. The resulting actions are surprisingly simple and elegant.