Gauged Supergravities from Spherical Reductions

Abstract

This dissertation is devoted to deriving the bosonic sectors of certain gauged supergravities in various dimensions from reducing eleven-dimensional supergravity, type IIA and type IIB supergravities in ten dimensions on certain spherical spaces. Explicit non-linear Kaluza-Klein ansätze for reductions of eleven-dimensional supergravity and of type IIA and type IIB supergravities on $S^n$ and $S^n\times T^m$ are presented. Knowing explicit non-linear ansätze is proven to be very useful in finding super Yang-Mills operators of gauge theories via AdS/CFT correspondence. We present a sample calculation which allows us to find a super Yang-Mills operator using a non-linear ansatz. Knowing non-linear ansätze is also useful for finding supergravity duals to certain twisted supersymmetric gauge theories. These supergravity solutions are branes wrapped on certain supersymmetric cycles. Some solutions, which are dual to gauge theories in three and five dimensions, are presented.

Ph.D. dessertation (Advisor: Christopher N. Pope)

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• Spinning and rotating strings for N=1 SYM theory and brane constructions
• Holographic current correlators at finite coupling and scattering off a supersymmetric plasma
• Glueballs, symmetry breaking and axionic strings in non-supersymmetric deformations of the Klebanov-Strassler background
• Stable de Sitter Vacua in 4 Dimensional Supergravity Originating from 5 Dimensions
• Phase transitions of an anisotropic N=4 super Yang-Mills plasma via holography
• A General Study of Ground States of N=2 Supergravity Theories with Symmetric Scalar Manifolds in 5 Dimensions