#### Title

Duality symmetries in string-inspired supergravity: T-dualities and the gauge/gravity correspondence

#### Document Type

Dissertation

#### Date of Degree

Spring 2015

#### Degree Name

PhD (Doctor of Philosophy)

#### Degree In

Physics

#### First Advisor

Vincent Rodgers

#### Abstract

Motivated by the AdS/CFT correspondence, new supersymmetric solutions to Type IIB and Type IIA supergravity are presented. These solutions contain $AdS_5$ or $AdS_4$ factors and are generated using T-duality symmetries of supergravity. The technique used to generate these solutions consists of performing a series of non-Abelian and Abelian T-dualities, sometimes with coordinate shifts in-between, to Freund-Rubin type seed backgrounds. An added bonus of the gauge fixing procedure inherent in non-Abelian T-Duality is the freedom to generate backgrounds with extra free parameters, some examples of which are presented. Aspects of the dual field theories of these new solutions are analyzed using holography techniques. The supersymmetry of these new backgrounds is also discussed.

In addition to supergravity backgrounds with AdS, the study of generalized Calabi-Yau manifolds in the context of flux compactifications is briefly reviewed. The particular case of the resolved cone over $Y^{p,q}$ and its admission of generalized SU(3) structure solutions is examined. Contrary to geometries with $AdS$ factors, whose field theory duals are conformal field theories, these types of geometries can be phenomenologically interesting to study, as their gauge theory duals are minimally supersymmetric and confining, thus they could someday help aid our understanding of strongly-coupled QCD (Quantum Chromodynamics).

#### Public Abstract

String theory is an important theoretical tool that unlike any other theory, incorporates gravity together with the other fundamental forces of nature. As a surprising byproduct, string theory is also able to describe two completely different theories, i.e. dual theories (or forces), in such a way that one may use the computational ease of one theory to extract nearly intractable calculations in its `dual' theory. The example that epitomizes this dual correspondence is the Anti-DeSitter/Conformal Field theory Correspondence aka AdS/CFT. The duals here are a quantum *gauge* field theory similar to nuclear physics in 4 dimensions and a classical *gravitational* theory in 5 dimensions. This correspondence provided insights into both theories that were previously unknown. In this thesis a more general correspondence now called the *gauge/gravity correspondence* is explored by exploiting very specific mathematical symmetry transformations on known gravitational theories to generate not only new solutions to gravitational field equations, but also identify new dual gauge theories associated with these new solutions. This work is expected to lend insight into some of the strongly interacting theories such as everyday nuclear physics.

#### Keywords

publicabstract, AdS/CFT, Flux Compactifications, gauge/gravity duality, String Theory, Supergravity, T-Dualities

#### Pages

xi, 103 pages

#### Bibliography

Includes bibliographical references (pages 98-103).

#### Copyright

Copyright 2015 Catherine Ann Whiting