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Register a new userSupergravity Actions with Integral Forms
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Added by
Pietro Antonio Grassi
Publication date
2014
fields
Physics
and research's language is
English
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Integral forms provide a natural and powerful tool for the construction of supergravity actions. They are generalizations of usual differential forms and are needed for a consistent theory of integration on supermanifolds. The group geometrical approach to supergravity and its variational principle are reformulated and clarified in this language. Central in our analysis is the Poincare dual of a bosonic manifold embedded into a supermanifold. Finally, using integral forms we provide a proof of Gates so-called Ectoplasmic Integration Theorem, relating superfield actions to component actions.
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We present few types of integral transforms and integral representations that are very useful for extending to supergeometry many familiar concepts of differential geometry. Among them we discuss the construction of the super Hodge dual, the integral representation of picture changing operators of string theories and the construction of the super-Liouville form of a symplectic supermanifold.
The superform construction of supergravity actions, christened the ectoplasm method, is based on the use of a closed super d-form in the case of d space-time dimensions. In known examples, such superforms are obtained by iteratively solving nontrivial cohomological problems. The latter usually makes this scheme no less laborious than the normal coordinate method for deriving component actions for matter-coupled supergravity. In this note we present an alternative procedure to generate required superforms in four space-time dimensions, which makes use of self-dual vector multiplets. It provides the shortest derivation of chiral actions in two different theories: (i) N = 1 old minimal supergravity; and (ii) N = 2 conformal supergravity. The N = 2 superform construction is developed here for the first time. Although our consideration is restricted to the case of four dimensions, a generalization to higher dimensions is plausible.
We present off-shell N=2 supergravity actions, which exhibit spontaneously broken local supersymmetry and allow for de Sitter vacua for certain values of the parameters. They are obtained by coupling the standard N=2 supergravity-matter systems to the Goldstino superfields introduced in arXiv:1105.3001 and arXiv:1607.01277 in the rigid supersymmetric case. These N=2 Goldstino superfields include nilpotent chiral and linear supermultiplets. We also describe a new reducible N=1 Goldstino supermultiplet.
We use exceptional field theory as a tool to work out the full non-linear reduction ansaetze for the AdS$_5times S^5$ compactification of IIB supergravity and its non-compact counterparts in which the sphere $S^5$ is replaced by the inhomogeneous hyperboloidal space $H^{p,q}$. The resulting theories are the maximal 5D supergravities with gauge groups SO(p,q). They are consistent truncations in the sense that every solution of 5D supergravity lifts to a solution of IIB supergravity. In particular, every stationary point and every holographic RG flow of the scalar potentials for the compact and non-compact 5D gaugings directly lift to solutions of IIB supergravity.
We perform a careful investigation of which p-form fields can be introduced consistently with the supersymmetry algebra of IIA and/or IIB ten-dimensional supergravity. In particular the ten-forms, also known as top-forms, require a careful analysis since in this case, as we will show, closure of the supersymmetry algebra at the linear level does not imply closure at the non-linear level. Consequently, some of the (IIA and IIB) ten-form potentials introduced in earlier work of some of us are discarded. At the same time we show that new ten-form potentials, consistent with the full non-linear supersymmetry algebra can be introduced. We give a superspace explanation of our work. All of our results are precisely in line with the predictions of the E(11) algebra.
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