S-duality, triangle groups and modular anomalies in N=2 SQCD

Understand

We study N = 2 superconformal theories with gauge group SU(N) and 2N fundamental flavours in a locus of the Coulomb branch with a Z_N symmetry.

• In this special vacuum, we calculate the prepotential, the dual periods and the period matrix using equivariant localization.
• When the flavours are massless, we find that the period matrix is completely specified by [N/2] effective couplings.
• On each of these, we show that the S-duality group acts as a generalized triangle group and that its hauptmodul can be used to write a non-perturbatively exact relation between each effective coupling and the bare one.