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This is a copy of the 2009 Princeton University thesis which examined variousaspects of gauge/gravity duality, including renormalization group flows, phasetransitions of the holographic entanglement entropy, and instabilitiesassociated with the breaking of supersymmetry. Chapter 5 contains newunpublished material on various instabilities of the weakly curvednon-supersymmetric $AdS_4$ backgrounds of M-theory.

Renormalization group flows in gauge-gravity duality