Dualisation of Dualities, II: Twisted self-duality of doubled fields and superdualities

TL;DR

The paper develops a doubled formalism for maximal supergravity theories, unifying gauge symmetries and dualities through a twisted self-duality condition on a superalgebra-valued field strength.

Contribution

It introduces a novel doubled formalism that captures all gauge symmetries and dualities in supergravity as a unified framework using superalgebras.

Findings

Formulation of equations of motion as twisted self-duality conditions.

Unification of gauge symmetries including U-dualities.

Representation of all gauge symmetries as subgroups of supergroups.

Abstract

We introduce a doubled formalism for the bosonic sector of the maximal supergravities, in which a Hodge dual potential is introduced for each bosonic field (except for the metric). The equations of motion can then be formulated as a twisted self-duality condition on the total field strength \G, which takes its values in a Lie superalgebra. This doubling is invariant under dualisations; it allows a unification of the gauge symmetries of all degrees, including the usual U-dualities that have degree zero. These ``superdualities'' encompass the dualities for all choices of polarisation (i.e. the choices between fields and their duals). All gauge symmetries appear as subgroups of finite-dimensional supergroups, with Grassmann coefficients in the differential algebra of the spacetime manifold.