Abstract

We will review the program of understanding 4d supersymmetric theories as dimensional reductions of 6d theories. In particular we will study compactifications on Riemann surfaces of N = (1, 0) 6d SCF Ts with a one dimensional tensor branch description as pure SU(3) gauge theory. We propose a field theory construction for the resulting 4d theories. We argue that the theories in four dimensions are quivers with SU(3) gauge nodes and free chiral fields. The conformal manifolds of the models are constructed from gauge couplings and baryonic superpotentials. We support our conjectures by matching the dimensions of the conformal manifolds with complex structure moduli of the Riemann surfaces, matching anomalies between six and four dimensions, and checking the dualities related to different pair of pants decompositions of the surfaces. As a simple application of the results we conjecture that SU(3) gauge theory with nine flavors in four dimensions has a duality group acting on the seven dimensional conformal manifold which is the mapping class group of sphere with ten marked points.