Superdualities: Below and beyond U-duality

TL;DR

This paper explores the structure and implications of superdualities, extending U-duality concepts in supergravity and string theories, highlighting their role in understanding symmetries, solutions, and nonperturbative effects.

Contribution

It introduces the concept of superdualities, embedding large symmetry groups into superalgebras, and demonstrates their invariance in all bosonic matter field equations of toroidally compactified supergravities.

Findings

Superdualities extend U-duality symmetries in supergravity.

Classical field equations are invariant under superdualities.

Potential extensions of superdualities are discussed.

Abstract

Hidden symmetries are the backbone of Integrable two-dimensional theories. They provide classical solutions of higher dimensional models as well, they seem to survive partially quantisation and their discrete remnants in M-theory called U-dualities, would provide a way to control infinities and nonperturbative effects in Supergravities and String theories. Starting from Einstein gravity we discuss the building blocks of these large groups of internal symmetries, and embed them in superalgebras of dynamical symmetries. The classical field equations for all bosonic matter fields of all toroidally compactified supergravities are invariant under such ``superdualities''. Possible extensions are briefly discussed.