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

TL;DR

The paper develops a universal doubled-field framework for maximal supergravity theories in diverse dimensions, expressing all bosonic equations of motion as twisted self-duality conditions on a total field strength $\mathcal{G}$ valued in a Lie (super)algebra. By pairing each field with a dual potential and organizing the resulting generators into a coset structure, the authors unify gauge and duality symmetries into a single algebraic scheme, typically a deformation of $G\ltimes G^*$. A key innovation is the introduction of a twelfth (fermionic) dimension, yielding a superalgebra that elegantly encodes the extended gauge structure; in the IIB case a purely bosonic algebra is recovered with careful handling of self-duality. The doubled formalism is then applied to scalar cosets, where global $G$ symmetry persists on the doubled field strengths and is realized (partially) on the dual potentials, with the framework extending to general cosets and sigma-models. Overall, the work provides a unifying, symmetry-rich description of dualities in maximal supergravity, illuminating the algebraic underpinnings of superdualities and their geometric realization via Iwasawa-like constructions.

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.