S-duality and the prepotential in 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 and C 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.

arXiv comment34 pages, LaTeX2e, version to be published in JHEP

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• Modular anomaly equations and S-duality in N=2 conformal SQCD
• Resumming instantons in N=2* theories with arbitrary gauge groups
• Aspects of Hecke Symmetry: Anomalies, Curves, and Chazy Equations
• Instanton Corrections for m and Omega
• BPS Equations in Omega-deformed N=4 Super Yang-Mills Theory