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Register a new userEnhanced Euclidean supersymmetry, 11D supergravity and $SU(infty)$ Toda equation
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We show how to lift solutions of Euclidean Einstein-Maxwell equations with non-zero cosmological constant to solutions of eleven-dimensional supergravity theory with non-zero fluxes. This yields a class of 11D metrics given in terms of solutions to $SU(infty)$ Toda equation. We give one example of a regular solution and analyse its supersymmetry. We also analyse the integrability conditions of the Killing spinor equations of N=2 minimal gauged supergravity in four Euclidean dimensions. We obtain necessary conditions for the existence of additional Killing spinors, corresponding to enhancement of supersymmetry. If the Weyl tensor is anti-self-dual then the supersymmetric metrics satisfying these conditions are given by separable solutions to the $SU(infty)$ Toda equation. Otherwise they are ambi-Kahler and are conformally equivalent to Kahler metrics of Calabi type or to product metrics on two Riemann surfaces.
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We establish an explicit correspondence between two--dimensional projective structures admitting a projective vector field, and a class of solutions to the $SU(infty)$ Toda equation. We give several examples of new, explicit solutions of the Toda equation, and construct their mini--twistor spaces. Finally we discuss the projective-to-Einstein correspondence, which gives a neutral signature Einstein metric on a cotangent bundle $T^*N$ of any projective structure $(N, [ abla])$. We show that there is a canonical Einstein of metric on an $R^*$--bundle over $T^*N$, with a connection whose curvature is the pull--back of the natural symplectic structure from $T^*N$.
We consider compactifications induced by the gravitino field of eleven dimensional supergravity. Such compactifications are not trivial in the sense that the gravitino profiles are not related to pure bosonic ones by means of a supersymmetry transformation. The basic property of such backgrounds is that they admit $psi$-torsion although they have vanishing Riemann tensor. Thus, these backgrounds may be considered also as solutions of the teleparallel formulation of supergravity. We construct two classes of solutions, one with both antisymmetric three-form field, gravity and gravitino and one with only gravity and gravitino. In these classes of solutions, the internal space is a parallelized compact manifold, so that it does not inherit any cosmological constant to the external spacetime. The latter turns out to be flat Minkowski in the maximally symmetric case. The elimination of the cosmological constant in the spontaneously compactified supergravity seems to be a generic property based on the trading of the cosmological constant for parallelizing torsion.
We propose a new construction of the supergravity inflation as an UV completion of the Higgs-$R^2$ inflation. In the dual description of $R^2$-supergravity, we show that there appear dual chiral superfields containing the scalaron or sigma field in the Starobinsky inflation, which unitarizes the supersymmetric Higgs inflation with a large non-minimal coupling up to the Planck scale. We find that a successful slow-roll inflation is achievable in the Higgs-sigma field space, but under the condition that higher curvature terms are introduced to cure the tachyonic mass problems for spectator singlet scalar fields. We also discuss supersymmetry breaking and its transmission to the visible sector as a result of the couplings of the dual chiral superfields and the non-minimal gravity coupling of the Higgs fields.
We classify super-symmetric solutions of the minimal $N=2$ gauged Euclidean supergravity in four dimensions. The solutions with anti-self-dual Maxwell field give rise to anti-self-dual Einstein metrics given in terms of solutions to the $SU(infty)$ Toda equation and more general three-dimensional Einstein--Weyl structures. Euclidean Kastor--Traschen metrics are also characterised by the existence of a certain super covariantly constant spinor.
In this paper we clarify the relations occurring among the osp(1|32) algebra, the M-algebra and the hidden superalgebra underlying the Free Differential Algebra of D=11 supergravity (to which we will refer as DF-algebra) that was introduced in the literature by DAuria and Fre in 1981 and is actually a (Lorentz valued) central extension of the M-algebra including a nilpotent spinor generator, Q. We focus in particular on the 4-form cohomology in 11D superspace of the supergravity theory, strictly related to the presence in the theory of a 3-form $A^{(3)}$. Once formulated in terms of its hidden superalgebra of 1-forms, we find that $A^{(3)}$ can be decomposed into the sum of two parts having different group-theoretical meaning: One of them allows to reproduce the FDA of the 11D Supergravity due to non-trivial contributions to the 4-form cohomology in superspace, while the second one does not contribute to the 4-form cohomology, being a closed 3-form in the vacuum, defining however a one parameter family of trilinear forms invariant under a symmetry algebra related to osp(1|32) by redefining the spin connection and adding a new Maurer-Cartan equation. We further discuss about the crucial role played by the 1-form spinor $eta$ (dual to the nilpotent generator Q) for the 4-form cohomology of the eleven dimensional theory on superspace.
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