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Gauged Supergravities from Spherical Reductions

Tuan A. Tran
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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.

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Tuan A. Tran. 2001-09-11. Gauged Supergravities from Spherical Reductions. https://arxiv.org/abs/hep-th/0109092

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