Compactification of 6D minimal SCFTs on Riemann surfaces

We study compactifications on Riemann surfaces with punctures of N=(1,0) six-dimensional SCFTs with a one-dimensional tensor branch and no continuous global symmetries. The effective description of such models on the tensor branch is in terms of pure gauge theories with decoupled tensor. For generic Riemann surfaces, the resulting theories in four dimensions are expected to have N=1 supersymmetry. We compute the anomalies expected from the resulting four-dimemsional theories by integrating the anomaly polynomial of the six-dimensional theory on the Riemann surface. For the cases with six-dimensional gauge models with gauge groups SU(3) and SO(8), we further propose a field theory construction for the resulting four-dimensional theories. For the six-dimensional SU(3) theory, we argue that the theories in four dimensions are quivers with SU(3) gauge nodes and free chiral fields. The theories one obtains from the six-dimensional SO(8) gauge theory are quivers with SU(4) gauge groups and chiral fields with R charge a half. In the last case, the theories constructed for general Riemann surfaces involve gauging of symmetries appearing at strong coupling. 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 pairs 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 the sphere with ten marked points.