Abstract
We derive a modular anomaly equation satisfied by the prepotential of the \( \mathcal{N}={2}^{\star } \) supersymmetric theories with non-simply laced gauge algebras, including the classical B r and C r infinite series and the exceptional F 4 and G 2 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 F 4 and G 2 theories are mapped into themselves (up to a rotation of the roots) in analogy with what happens for the \( \mathcal{N}=4 \) supersymmetric theories. These results extend the analysis for the simply laced groups presented in a companion paper.
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Billó, M., Frau, M., Fucito, F. et al. S-duality and the prepotential of \( \mathcal{N}={2}^{\star } \) theories (II): the non-simply laced algebras. J. High Energ. Phys. 2015, 26 (2015). https://doi.org/10.1007/JHEP11(2015)026
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DOI: https://doi.org/10.1007/JHEP11(2015)026