  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.
