The * report 1 The * report

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 = ± 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 κ -symmetry, consistent with such backgrounds. We also give general algebraic descrip-tions of such ‘star’ theories, so that they can be identified as representatives of some of the equivalence classes of κ -invariant Green-Schwarz actions.