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arXiv · 1507.07709

S-duality and the prepotential in N=2* theories (I): the ADE algebras

M. Billo·M. Frau·F. Fucito·A. Lerda·J. F. Morales
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Abstract

The prepotential of N=2* supersymmetric theories with unitary gauge groups in an Omega-background satisfies a modular anomaly equation that can be recursively solved order by order in an expansion for small mass. By requiring that S-duality acts on the prepotential as a Fourier transform we generalise this result to N=2* theories with gauge algebras of the D and E type and show that their prepotentials can be written in terms of quasi-modular forms of SL(2,Z). The results are checked against microscopic multi-instanton calculus based on localization for the A and D series and reproduce the known 1-instanton prepotential of the pure N=2 theories for any gauge group of ADE type. Our results can also be used to obtain the multi-instanton terms in the exceptional theories for which the microscopic instanton calculus and the ADHM construction are not available.

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M. Billo, M. Frau, F. Fucito, A. Lerda, J. F. Morales. 2015-10-22. S-duality and the prepotential in N=2* theories (I): the ADE algebras. https://arxiv.org/abs/1507.07709

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