Modular anomaly equations and S-duality in N = 2 conformal SQCD

Abstract: We use localization techniques to study the non-perturbative properties of an N = 2 superconformal gauge theory with gauge group SU(3) and six fundamental flavours. The instanton corrections to the prepotential, the dual periods and the period matrix are calculated in a locus of special vacua possessing a ℤ₃symmetry. In a semiclassical expansion, we show that these observables are constrained by S-duality via a modular anomaly equation which takes the form of a recursion relation. The solutions of the recursion relation are quasi-modular functions of Γ₁(3), which is a subgroup of the S-duality group and is also a congruence subgroup of SL(2, ℤ).