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

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 B_r and C_r 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.