The operator product expansion for "small" Wilson loops in N = 4, d = 4 SYM is studied. The OPE coefficients are calculated in the large N and g 2 YM N limit by exploiting the AdS/CFT correspondence. We also consider Wilson surfaces in the (0, 2), d = 6 superconformal theory. In this case, we find that the UV divergent terms include a term proportional to the rigid string action.

We find M -theory solutions that are holographic duals of flows of the maximally supersymmetric (N = 8) scalar-fermion theory in (2 + 1) dimensions. In particular, we construct the M -theory solution dual to a flow in which a single chiral multiplet is given a mass, and the theory goes to a new infra-red fixed point. We also examine this new solution using M 2-brane probes. The (2 + 1)-dimensional field theory fixed-point is closely related to that of Leigh and Strassler, while the M -theory solution is closely related to the corresponding IIB flow solution. We recast the IIB flow solution in a more geometric manner and use this to obtain an Ansatz for the M -theory flow. We are able to generalize our solution further to obtain flows with del Pezzo sub-manifolds, and we give an explicit solution with a conifold singularity.

We apply the proposal of Dijkgraaf and Vafa to analyze N = 1 gauge theory with SO(N) and Sp(N) gauge groups with arbitrary tree-level superpotentials using matrix model techniques. We derive the planar and leading non-planar contributions to the large M SO(M) and Sp(M) matrix model free energy by applying the technology of higher-genus loop equations and by straightforward diagrammatics. The loop equations suggest that the RP 2 free energy is given as a derivative of the sphere contribution, a relation which we verify diagrammatically. With a refinement of the proposal of Dijkgraaf and Vafa for the effective superpotential, we find agreement with field theory expectations.

The group SO(5,2) contains an obvious SO(3)ϫSO(2) ϫSO(2) and the SU(2) R gauge symmetry of the supergravity is to be identified with the SO(3), while the U(1) gauge symmetry is the diagonal subgroup of SO(2)ϫSO (2).It is also worth remembering that this SU(2) R ϫU(1) commutes with an SU(1,1) in SO(5,2), and that this SU(1,1) is naturally identified with the SU(1,1) of the dilaton and axion in the original type IIB theory. The supergrav-

We compute the two and three-point correlation functions of chiral primary operators in the large N limit of the (0, 2), d = 6 superconformal theory. We also consider the operator product expansion of Wilson surfaces in the (0, 2) theory and compute the OPE coefficients of the chiral primary operators at large N from the correlation functions of surfaces.