Duality symmetries in supergravity: New structures and deformations

Abstract

Maximal supergravity theories in 2 < D < 10 dimensions are known to possess intriguing global symmetries, known as duality symmetries, which can be optionally broken by turning on non-abelian gauge interactions. Many of these theories can be obtained from various truncations of eleven and/or ten-dimensional maximal supergravities in the context of dimensional compactification. In this thesis, we explore the unifying abilities and/or the higher-dimensional manifestations of these duality symmetries through various (re)formulations of supergravity theories. In a first chapter we present a reformulation of type IIB supergravity, in which the supersymmetry transformation rules reflect the characteristic E6(6) multiplet structures of five-dimensional maximal supergravities in the embedding tensor formalism. In particular, by including the dual six-form in the IIB theory, the E6(6) vector-tensor hierarchy is shown to emerge in a ten-dimensional context. This reformulation ultimately allows us to study the consistency of the truncation of IIB supergravity compactified on the five-sphere to SO(6) gauged supergravity. The second chapter deals with exceptional field theory (EFT), which relies on an enlarged spacetime in order to embed the massless type II and eleven-dimensional supergravities into a formally duality covariant framework. The physical theories are recovered as solutions of a so-called section constraint and their gauge transformations are encoded in a generalised Lie derivative. We present an extension of the EFT framework by introducing consistent deformations of its generalised Lie derivative. In particular, we show that for a specific deformation, massive type IIA supergravity is reproduced for the first time as a solution of the section constraint. Finally, the tensor hierarchy and the gauge invariant (pseudo)-action of the deformed E7(7) theory are constructed explicitly. In the last chapter, we study N=4 conformal supergravity in four dimensions. In contrast with the N < 4 cases, this maximal theory contains scalar fields that parametrise an SU(1,1)/U(1) coset space. The N=4 Weyl supermultiplet and its off-shell non-linear superconformal transformation rules have been derived long ago, but so far a complete action was not known. We construct a density formula which captures the most general class of N=4 conformal supergravity actions. The latter turn out to depend on a single holomorphic function that is homogeneous of zeroth degree in the coset scalars. We present explicitly their bosonic terms and comment on potential future applications of this result.