AdS4_4 solutions of massive IIA from dyonic ISO(7) supergravity

Explicit formulae are given for the consistent truncation of massive type IIA supergravity on the six-sphere to the SU(3)--invariant sector of $D=4$ ${\cal N}=8$ supergravity with dyonic ISO(7) gauging. These formulae are then used to construct AdS$_4$ solutions of massive type IIA via uplift on $S^6$ of the critical points of the $D=4$ supergravity with at least SU(3) symmetry. We find a new ${\cal N}=1$ solution with SU(3) symmetry, a new non-supersymmetric solution with SO(6) symmetry, and recover previously known solutions. We quantise the fluxes, calculate the gravitational free energies of the solutions and discuss the stability of the non-supersymmetric ones. Among these, a (previously known) G$_2$--invariant solution is found to be stable.Comment: 30 pages; v2: a few typos corrected and reference added; v3: A few clarifications and reference added. Version published in JHEP03(2016)07

Dyonic ISO(7) supergravity and the duality hierarchy

Motivated by its well defined higher dimensional origin, a detailed study of $D=4$ $\mathcal{N}=8$ supergravity with a dyonically gauged $\textrm{ISO}(7) = \textrm{SO}(7) \ltimes \mathbb{R}^7$ gauge group is performed. We write down the Lagrangian and describe the tensor and duality hierarchies, focusing on an interesting subsector with closed field equations and supersymmetry transformations. We then truncate the $\mathcal{N}=8$ theory to some smaller sectors with $\mathcal{N}=2$ and $\mathcal{N}=1$ supersymmetry and SU(3), $\textrm{G}_2$ and SO(4) bosonic symmetry. Canonical and superpotential formulations for these sectors are given, and their vacuum structure and spectra is analysed. Unlike the purely electric ISO(7) gauging, the dyonic gauging displays a rich structure of vacua, all of them AdS. We recover all previously known ones and find a new $\mathcal{N}=1$ vacuum with SU(3) symmetry and various non-supersymmetric vacua, all of them stable within the full $\mathcal{N}=8$ theory.Comment: 52 pages, 4 tables. v2: Section 2.4 on critical points added. v3: Version published in JHE

Universal Kaluza-Klein reductions of type IIB to N=4 supergravity in five dimensions

We construct explicit consistent Kaluza-Klein reductions of type IIB supergravity on HK_4 x S^1, where HK_4 is an arbitrary four-dimensional hyper-Kaehler manifold, and on SE5, an arbitrary five-dimensional Sasaki-Einstein manifold. In the former case we obtain the bosonic action of D=5 N=4 (ungauged) supergravity coupled to two vector multiplets. For the SE_5 case we extend a known reduction, which leads to minimal D=5 N=2 gauged supergravity, to also include a multiplet of massive fields, containing the breathing mode of the SE_5. We show that the resulting D=5 action is also consistent with N=4 gauged supergravity coupled to two vector multiplets. This theory has a supersymmetric AdS_5 vacuum, which uplifts to the class of supersymmetric AdS_5 x SE_5 solutions, that spontaneously breaks N=4 to N=2, and also a non-supersymmetric AdS_5 vacuum which uplifts to a class of solutions first found by Romans.Comment: 1+34 pages. v2: Minor typos corrected, three references added. Version to be published in JHE

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

Symmetry and holonomy in M Theory

In this PhD Thesis, supersymmetry and its formulation in the context of D=11 supergravity is discussed from several perspectives. The role of generalized holonomy as a classification tool of supersymmetric supergravity solutions is reviewed, with particular emphasis on how successive supercovariant derivatives of the generalized curvature may be needed to properly define the generalized holonomy algebra. The generalized curvature is also shown to contain the supergravity equations of motion, even in the non-vanishing gravitino case. The underlying gauge symmetry of D=11 supergravity is discussed and argued to become manifest when its three-form field A_3 is expressed through a set of one-form gauge fields, associated with the generators of a suitable family of enlarged supersymmetry algebras. This family is related to osp(1|32) through expansion, a method to obtain new Lie (super)algebras of increasing dimensions from given ones. The analysis of the underlying gauge symmetry of D=11 supergravity leads naturally to enlarged supersymmetry algebras and superspaces making, thus, natural to consider actions for objects moving in such spaces. In particular, a string moving in tensorial space is discussed, describing the excitations of a state preserving 30 out of 32 supersymmetries (hence composed of two preons, hypothetical constituents of M Theory preserving 31 supersymmetries). A G-frame method is also discussed to study hypothetical preonic solutions of supergravity.Comment: PhD Thesis (Advisor: J.A. de Azcarraga). 16+201 page