S-duality and the prepotential of N = 2⋆ theories (II): the non-simply laced algebras

Abstract

Abstract: We derive a modular anomaly equation satisfied by the prepotential of the N = 2⋆ supersymmetric theories with non-simply laced gauge algebras, including the classical Br and Cr infinite series and the exceptional F4 and G2 cases. This equation determines the exact prepotential recursively in an expansion for small mass in terms of quasi-modular forms of the S-duality group. We also discuss the behaviour of these theories under S-duality and show that the prepotential of the SO(2r + 1) theory is mapped to that of the Sp(2r) theory and viceversa, while the exceptional F4 and G2 theories are mapped into themselves (up to a rotation of the roots) in analogy with what happens for the N = 4 supersymmetric theories. These results extend the analysis for the simply laced groups presented in a companion paper.