The AdS/CFT Correspondence and Symmetry Breaking

In the first part of this thesis we study baryonic U(1) symmetries dual to Betti multiplets in the AdS_4/CFT_3 correspondence for M2 branes at Calabi-Yau 4-fold singularities. We begin by focusing on isolated toric singularities without vanishing 6-cycles, which we classify, and propose for them field theory duals. We then study in detail the cone over Q^111 and find agreement between the spectrum of baryonic operators in this theory and M5 branes wrapping 5-cycles in the Q^111 space. The physics of vacua in which these symmetries are spontaneously broken precisely matches a dual gravity analysis involving resolutions of the singularity, where we are able to match condensates, Goldstone bosons and global strings. We then study the implications of turning on a torsion 4-form flux. This flux non-trivially affects the supergravity dual of Higgsing, and we show that the supergravity and field theory analyses precisely match in an example based on Y^12(CP^2). We then explain how the choice of M-theory circle can result in exotic renormalization group flows. We also argue that theories where the resolutions have 6-cycles are expected to receive non-perturbative corrections from M5 instantons. We give a general formula relating the instanton action to normalizable harmonic 2-forms. In the second part of this thesis we study the breaking of baryonic symmetries in the AdS_5/CFT_4 correspondence. This leads, for particular vacuum expectation values, to the emergence of baryonic symmetries during the renormalization group flow. We identify these vacuum expectation values with critical values of the B-field moduli in the dual supergravity backgrounds. We study in detail the C^3/Z_3 orbifold theory and the dual supergravity backgrounds that correspond to the breaking of the emerging baryonic symmetries, and identify the expected Goldstone bosons and global strings in the IR