We compute the circular Wilson loop of N = 4 SYM theory at large N in the rank k symmetric and antisymmetric tensor representations. Using a quadratic Hermitian matrix model we obtain expressions for all values of the 't Hooft coupling. At large and small couplings we give explicit formulae and reproduce supergravity results from both D3 and D5 branes within a systematic framework.

We consider an O(N) model coupled self-consistently to gravity in the semiclassical approximation, where the field is subject to ''new inflation'' type initial conditions. We study the dynamics self-consistently and non-perturbatively with non-equilibrium field theory methods in the large N limit. We find that spinodal instabilities drive the growth of non-perturbatively large quantum fluctuations which shut off the inflationary growth of the scale factor. We find that a very specific combination of these large fluctuations plus the inflaton zero mode assemble into a new effective field. This new field behaves classically and it is the object which actually rolls down. We show how this reinterpretation saves the standard picture of how metric perturbations are generated during inflation and that the spinodal growth of fluctuations dominates the time dependence of the Bardeen variable for superhorizon modes during inflation. We compute the amplitude and index for the spectrum of scalar density and tensor perturbations and argue that in all models of this type the spinodal instabilities are responsible for a ''red'' spectrum of primordial scalar density perturbations. A criterion for the validity of these models is provided and contact with the reconstruction program is established validating some of the results within a non-perturbative framework. The decoherence aspects and the quantum to classical transition through inflation are studied in detail by following the full evolution of the density matrix and relating the classicality of cosmological perturbations to that of long-wavelength matter fluctuations.

We investigate an exactly marginal N = 1 supersymmetric deformation of SU(N) N = 4 supersymmetric Yang-Mills theory discovered by Leigh and Strassler. We use a matrix model to compute the exact superpotential for a further massive deformation of the U(N) Leigh-Strassler theory. We then show how the exact superpotential and eigenvalue spectrum for the SU(N) theory follows by a process of integrating-in. We find that different vacua are related by an action of the SL(2, Z) modular group on the bare couplings of the theory extending the action of electric-magnetic duality away from the N = 4 theory. We perform non-trivial tests of the matrix model results against semiclassical field theory analysis. We also show that there are interesting points in parameter space where condensates can diverge and vacua disappear. Based on the matrix model results, we propose an exact elliptic superpotential to describe the theory compactified on a circle of finite radius.1 One such deformation has been analysed recently using matrix models in [3].

Dijkgraaf and Vafa (DV) have conjectured that the exact superpotential for a large class of N = 1 SUSY gauge theories can be extracted from the planar limit of a certain holomorphic matrix integral. We test their proposal against existing knowledge for a family of deformations of N = 4 SUSY Yang-Mills theory involving an arbitrary polynomial superpotential for one of the three adjoint chiral superfields. Specifically, we compare the DV prediction for these models with earlier results based on the connection between SUSY gauge theories and integrable systems. We find complete agreement between the two approaches. In particular we show how the DV proposal allows the extraction of the exact eigenvalues of the adjoint scalar in the confining vacuum and hence computes all related condensates of the finite-N gauge theory. We extend these results to include Leigh-Strassler deformations of the N = 4 theory.

We study the expectation value of a Polyakov-Maldacena loop that wraps the thermal circle k times in strongly coupled N = 4 super Yang-Mills theory. This is achieved by considering probe D3 and D5 brane embeddings in the dual black hole geometry. In contrast to multiply wound spatial Wilson loops, nontrivial dependence on k is captured through D5 branes. We find N −2/3 corrections, reminiscent of the scaling behaviour near a Gross-Witten transition.

Abstract:We examine the thermodynamic properties of recently constructed black hole solutions in SL(3, R) × SL(3, R) Chern-Simons theory in the presence of a chemical potential for spin-3 charge, which acts as an irrelevant deformation of the dual CFT with W 3 × W 3 symmetry. The smoothness or holonomy conditions admit four branches of solutions describing a flow between two AdS 3 backgrounds corresponding to two different CFTs. The dominant branch at low temperatures, connected to the BTZ black hole, merges smoothly with a thermodynamically unstable branch and disappears at higher temperatures. We confirm that the UV region of the flow satisfies the Ward identities of a CFT with W (2) 3 × W (2) 3 symmetry deformed by a spin-3 2 current. This allows to identify the precise map between UV and IR thermodynamic variables. We find that the high temperature regime is dominated by a black hole branch whose thermodynamics can only be consistently inferred with reference to this W (2) 3 × W (2) 3 CFT.

We calculate the exact values of the holomorphic observables of N = 4 supersymmetric SU(N) Yang-Mills theory deformed by mass terms which preserve N = 1 SUSY. These include the chiral condensates in each massive vacuum of the theory as well as the central charge which determines the tension of BPS saturated domain walls interpolating between these vacua. Several unexpected features emerge in the large-N limit, including anomalous modular properties under an SL(2, Z) duality group which acts on a complexification of the 't Hooft coupling λ = g 2 N/4π. We discuss our results in the context of the AdS/CFT correspondence.

We study relevant deformations of the N = 2 superconformal theory on the world-volume of N D3 branes at an A k−1 singularity. In particular, we determine the vacuum structure of the mass-deformed theory with N = 1 supersymmetry and show how the different vacua are permuted by an extended duality symmetry. We then obtain exact, modular covariant formulae (for all k, N and arbitrary gauge couplings) for the holomorphic observables in the massive vacua in two different ways: by lifting to M-theory, and by compactification to three dimensions and subsequent use of mirror symmetry. In the latter case, we find an exact superpotential for the model which coincides with a certain combination of the quadratic Hamiltonians of the spin generalization of the elliptic Calogero-Moser integrable system.