The *Report

TL;DR

This paper develops component and superspace formulations for the Type IIA* supergravity, revealing how it differs from the conventional theory and providing a supersymmetric Green-Schwarz action compatible with its backgrounds.

Contribution

It introduces a superspace description of Type IIA* supergravity, showing how to interpolate between IIA and IIA* theories and constructing a consistent Green-Schwarz action with -symmetry.

Findings

Superspace formulation of Type IIA* supergravity established.

A parameter interpolates between IIA and IIA* theories in superspace.

Green-Schwarz action with -symmetry constructed for these backgrounds.

Abstract

We present component and superspace formulations for the recently-proposed Type IIA* (or so-called `star') supergravity theory, which is timelike dual to the conventional Type IIB theory. First, within the component approach, all terms in the action are fixed up to the quartic fermionic ones. As desired, the kinetic terms for Ramond-Ramond fields have signs opposite to the conventional case. Consistency of these are then insured by the construction of a superspace description of this theory. As a by-product, we find that a single signature parameter $s = \pm 1$ can interpolate the Type IIA and Type IIA* theories in superspace. This superspace result naturally allows us to present a Green-Schwarz action, that possesses $\kappa$-symmetry, consistent with such backgrounds. We also give general algebraic descriptions of such `star' theories, so that they can be identified as representatives of some of the equivalence classes of $\kappa$-invariant Green-Schwarz actions.