The exceptional story of massive IIA supergravity

The framework of exceptional field theory is extended by introducing consistent deformations of its generalised Lie derivative. For the first time, massive type IIA supergravity is reproduced geometrically as a solution of the section constraint. This provides a unified description of all ten- and eleven-dimensional maximal supergravities. The action of the E7 deformed theory is constructed, and reduces to those of exceptional field theory and gauged maximal supergravity in respective limits. The relation of this new framework to other approaches for generating the Romans mass non-geometrically is discussed.Comment: 39 pages. v2: typos corrected, references added. v3: typos corrected, references added, published versio

IIB Supergravity and the E6(6) covariant vector-tensor hierarchy

IIB supergravity is reformulated with a manifest local USp(8) invariance that makes the embedding of five-dimensional maximal supergravities transparent. In this formulation the ten-dimensional theory exhibits all the 27 one-form fields and 22 of the 27 two-form fields that are required by the vector-tensor hierarchy of the five-dimensional theory. The missing 5 two-form fields must transform in the same representation as a descendant of the ten-dimensional `dual graviton'. The invariant E6(6) symmetric tensor that appears in the vector-tensor hierarchy is reproduced. Generalized vielbeine are derived from the supersymmetry transformations of the vector fields, as well as consistent expressions for the USp(8) covariant fermion fields. Implications are discussed for the consistency of the truncation of IIB supergravity compactified on the five-sphere to maximal gauged supergravity in five space-time dimensions with an SO(6) gauge group.Comment: 48 pages, added an extra affiliatio

Consistent truncation of eleven-dimensional supergravity on S8×S1S^8\times S^1

Eleven-dimensional supergravity on $S^8\times S^1$ is conjectured to be dual to the M-theory matrix model. We prove that the dynamics of a subset of fluctuations around this background is consistently described by D=2 SO(9) gauged maximal supergravity. We provide the full non-linear uplift formulae for all bosonic fields. We also present a further truncation to the SO(3)$\times$SO(6) invariant sector and discuss its relation to the BMN matrix model at finite temperature. The construction relies on the framework of generalised Scherk-Schwarz reductions, established for E$_9$ exceptional field theory in a companion paper. As a by-product, we severely constrain the most general gauge deformations in D=2 admitting an uplift to higher dimensions.Comment: 40 pages + appendice

Maximal D=2 supergravities from higher dimensions

We develop in detail the general framework of consistent Kaluza-Klein truncations from D=11 and type II supergravities to gauged maximal supergravities in two dimensions. In particular, we unveil the complete bosonic dynamics of all gauged maximal supergravities that admit a geometric uplift. Our construction relies on generalised Scherk-Schwarz reductions of E$_9$ exceptional field theory. The application to the reduction of D=11 supergravity on $S^8\times S^1$ to SO(9) gauged supergravity is presented in a companion paper.Comment: 46 pages plus appendice

N=4 conformal supergravity: the complete actions

The most general class of 4D N=4 conformal supergravity actions depends on a holomorphic function of the scalar fields that parametrize an SU(1,1)/U(1) coset space. The bosonic sector of these actions was presented in a letter [arXiv:1609.09083]. Here we provide the complete actions to all orders in the fermion fields. They rely upon a new N=4 density formula, which permits a direct but involved construction. This density formula also recovers the on-shell action for vector multiplets coupled to conformal supergravity. Applications of these results in the context of Poincar\'e supergravity are briefly discussed.Comment: v2: 44 pages, supplementary file added to ancillary file

Duality symmetries in supergravity : New structures and deformations

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

Duality symmetries in supergravity : New structures and deformations

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