Resumming instantons in N=2* theories with arbitrary gauge groups

Abstract

We discuss the modular anomaly equation satisfied by the the prepotential of 4-dimensional N=2* theories and show that its validity is related to S-duality. The recursion relations that follow from the modular anomaly equation allow one to write the prepotential in terms of (quasi)-modular forms, thus resumming the instanton contributions. These results can be checked against the microscopic multi-instanton calculus in the case of classical algebras, but are valid also for the exceptional E6, E7, E8, F4 and G2 algebras, where direct computations are not available.

14 pages. To appear in the Proceedings of the XIV Marcel Grossmann Meeting, Rome, Italy, July 12-18, 2015. V2: aknowledgments added

References in corpus (6)

• Seiberg-Witten Theory and Random Partitions
• Seiberg-Witten prepotential from instanton counting
• 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
• S-duality and the prepotential in N=2* theories (I): the ADE algebras
• Modular anomaly equations and S-duality in N=2 conformal SQCD

Cited by in corpus (6)

• A slow review of the AGT correspondence
• Integrated correlators in $\mathcal{N}=4$ super Yang-Mills and periods
• S-duality, triangle groups and modular anomalies in N=2 SQCD
• Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2$ theories
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours
• Instanton Corrections for m and Omega