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

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.

33 pages, LaTeX2e, added references, version to be published in JHEP

References in corpus (5)

• S-duality as a beta-deformed Fourier transform
• Topological Strings and (Almost) Modular Forms
• Alpha- and Omega-Deformations from fluxes in M-Theory
• S-duality and the prepotential in N=2* theories (II): the non-simply laced algebras
• Modular anomaly equations and S-duality in N=2 conformal SQCD

Cited by in corpus (9)

• 5d/6d DE instantons from trivalent gluing of web diagrams
• Integrated correlators in $\mathcal{N}=4$ super Yang-Mills and periods
• S-duality and the prepotential in N=2* theories (II): the non-simply laced algebras
• S-duality, triangle groups and modular anomalies in N=2 SQCD
• $\mathcal{N}=2^{\star }$ from Topological Amplitudes in String Theory
• Modular anomaly equations and S-duality in N=2 conformal SQCD
• Resumming instantons in N=2* theories with arbitrary gauge groups
• Instanton Corrections for m and Omega
• BPS Equations in Omega-deformed N=4 Super Yang-Mills Theory