S-duality, triangle groups and modular anomalies in N=2 SQCD

Abstract

We study N = 2 superconformal theories with gauge group SU(N) and 2N fundamental flavours in a locus of the Coulomb branch with a Z_N symmetry. In this special vacuum, we calculate the prepotential, the dual periods and the period matrix using equivariant localization. When the flavours are massless, we find that the period matrix is completely specified by [N/2] effective couplings. On each of these, we show that the S-duality group acts as a generalized triangle group and that its hauptmodul can be used to write a non-perturbatively exact relation between each effective coupling and the bare one. For N = 2, 3, 4 and 6, the generalized triangle group is an arithmetic Hecke group which contains a subgroup that is also a congruence subgroup of the modular group PSL(2,Z). For these cases, we introduce mass deformations that respect the symmetries of the special vacuum and show that the constraints arising from S-duality make it possible to resum the instanton contributions to the period matrix in terms of meromorphic modular forms which solve modular anomaly equations.

50 pages, 1 figure; a few references added; to be published in JHEP

References in corpus (9)

• 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
• Modular anomaly equations in N=2* theories and their large-N limit
• Quantum geometry from the toroidal block
• 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
• Modular anomaly equations and S-duality in N=2 conformal SQCD
• Resumming instantons in N=2* theories with arbitrary gauge groups

Cited by in corpus (14)

• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• A slow review of the AGT correspondence
• Exact WKB Analysis of N = 2 Gauge Theories
• Elliptic Loci of SU(3) Vacua
• On the large $\Omega$-deformations in the Nekrasov-Shatashvili limit of $\mathcal{N}=2^{\ast }$ SYM
• Chiral observables and S-duality in N = 2* U(N) gauge theories
• Exact partition functions for the $\Omega$-deformed $\mathcal{N}=2^{\ast }$ $SU(2)$ gauge theory
• On Chebyshev Wells: Periods, Deformations, and Resurgence
• Resumming instantons in N=2* theories with arbitrary gauge groups
• Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2$ theories
• Aspects of Hecke Symmetry: Anomalies, Curves, and Chazy Equations
• Effective Gravitational Couplings of Higher-Rank Supersymmetric Gauge Theories
• Aspects of Hecke Symmetry I: Ramanujan Identities and Inversion Formulas
• Triangle Groups: Automorphic Forms and Nonlinear Differential Equations