Title:

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 CalabiYau fourfold singularities. Such short multiplets originate from the KaluzaKlein compactification of elevendimensional supergravity on the corresponding SasakiEinstein sevenmanifolds. Analysis of the boundary conditions for vector fields in AdS_4 allows for a choice where wrapped M5 brane states carrying nonzero charge under such symmetries can be considered. We begin by focusing on isolated toric singularities without vanishing sixcycles, which we classify, and propose for them field theory duals. We then study in detail the cone over the wellknown SasakiEinstein space Q^111, which is a U(1) fibration over CP^1 x CP^1 x CP^1. The boundary conditions considered are dual to a CFT where the gauge group is U(1)^2 x SU(N)^4. We find agreement between the spectrum of gaugeinvariant baryonictype operators in this theory and M5 branes wrapping fivecycles in the Q^111 space. Moreover, 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 of the baryonic operators, Goldstone bosons and global strings. We then study the implications of turning on a closed threeform with nonzero periods through torsion three cycles in the SasakiEinstein manifold. This threeform, otherwise known as torsion Gflux, nontrivially affects the supergravity dual of Higgsing, and we show that the supergravity and field theory analyses precisely match in an example based on the SasakiEinstein manifold Y^1,2(CP^2), which is a S^3 bundle over CP^2. We then explain how the choice of Mtheory circle in the background can result in exotic renormalization group flows in the dual field theory, and study this in detail for the SasakiEinstein manifold Y^1,2(CP^2). We also argue more generally that theories where the resolutions have sixcycles are expected to receive nonperturbative corrections from M5 brane instantons. We give a general formula relating the instanton action to normalizable harmonic twoforms, and compute it explicitly for the SasakiEinstein Q^222 example, which is a Z_2 orbifold of Q^111 in which the free Z_2 quotient is along the Rsymmetry U(1) fibre. The holographic interpretation of such instantons is currently unclear. In the second part of this thesis we study the breaking of baryonic symmetries in the AdS_5/CFT_4 correspondence for D3 branes at CalabiYau threefold singularities. This leads, for particular vacuum expectation values, to the emergence of nonanomalous baryonic symmetries during the renormalization group flow. We identify these vacuum expectation values with critical values of the NSNS Bfield 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 infrared. In doing so we confirm the claim that the emerging symmetries are indeed nonanomalous baryonic symmetries.
