DUALITY IN SUPERGRAVITY THEORIES

The target space dynamics of supermembrane (and superstring) theories is described by supergravity theories. Supergravity theories associated to dual supermembrane theories live in the same space-time dimension and are themselves dual to each other. We present a unified treatment in superspace of the two dual formulations of D = 10, N = 1 pure supergravity based on a strictly super-geometrical framework: the only fundamental objects are the super Riemann curvature and torsion, and the related Bianchi identities are sufficient to set the theory on shell; there is no need to introduce, from the beginning, closed three-or seven-superforms. This formulation extends also to non-minimal models. Moreover, in this framework the algebraic analogy between pure super Yang-Mills theoriesand pure supergravity in D = 10 is manifest. As an additional outcome in the present formulation the supersymmetric partner of the ABBJ-Lorentz anomaly in pure D = 10 supergravity can be computed in complete analog...