Large-N volume independence in conformal and confining gauge theories

Consequences of large N volume independence are examined in conformal and confining gauge theories. In the large N limit, gauge theories compactified on Rd-k x (S-1)(k) are independent of the S-1 radii, provided the theory has unbroken center symmetry. In particular, this implies that a large N gauge theory which, on R-d, flows to an IR fixed point, retains the infinite correlation length and other scale invariant properties of the decompactified theory even when compactified on Rd-k x (S-1)(k). In other words, finite volume effects are 1/N suppressed. In lattice formulations of vector-like theories, this implies that numerical studies to determine the boundary between confined and conformal phases may be performed on one-site lattice models. In N = 4 supersymmetric Yang-Mills theory, the center symmetry realization is a matter of choice: the theory on R4-k x (S-1)(k) has a moduli space which contains points with all possible realizations of center symmetry. Large N QCD with massive adjoint fermions and one or two compactified dimensions has a rich phase structure with an in finite number of phase transitions coalescing in the zero radius limit.