Modular anomaly equations and S-duality in N=2 conformal SQCD

Abstract

We use localization techniques to study the non-perturbative properties of an N=2 superconformal gauge theory with gauge group SU(3) and six fundamental flavours. The instanton corrections to the prepotential, the dual periods and the period matrix are calculated in a locus of special vacua possessing a Z_3 symmetry. In a semi-classical expansion, we show that these observables are constrained by S-duality via a modular anomaly equation which takes the form of a recursion relation. The solutions of the recursion relation are quasi-modular functions of Gamma_1(3), which is a subgroup of the S-duality group and is also a congruence subgroup of SL(2,Z).

30 pages, 2 figures, references added, typos fixed

References in corpus (5)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• S-duality in N=2 supersymmetric gauge theories
• S-duality and the prepotential in N=2* theories (II): the non-simply laced algebras
• Non-perturbative studies of N=2 conformal quiver gauge theories
• S-duality and the prepotential in N=2* theories (I): the ADE algebras

Cited by in corpus (8)

• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• S-duality, triangle groups and modular anomalies in N=2 SQCD
• S-duality and the prepotential in N=2* theories (II): the non-simply laced algebras
• S-duality and the prepotential in N=2* theories (I): the ADE algebras
• On Chebyshev Wells: Periods, Deformations, and Resurgence
• Resumming instantons in N=2* theories with arbitrary gauge groups
• New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential
• Aspects of Hecke Symmetry: Anomalies, Curves, and Chazy Equations