Integrability of RG flows and duality in three dimensions in the 1/N expansion

I study some classes of RG flows in three dimensions that are classically conformal and have manifest g --> 1/g dualities. The RG flow interpolates between known (four-fermion, Wilson-Fischer, phi(3)(6)) and new interacting fixed points. These models have two remarkable properties: (i) the RG flow can be integrated for arbitrarily large values of the couplings g at each order of the 1/N expansion; (ii) the duality symmetries are exact at each order of the 1/N expansion. I integrate the RG flow explicitly to the order O(1/N), write correlators at the leading-log level and study the interpolation between the fixed points. I examine how duality is implemented in the regularized theory and verified in the results of this paper. (C) 2003 Elsevier Science B.V. All rights reserved.