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 (35)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• N=2 dualities
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• The Coulomb Phase of N=2 Supersymmetric QCD
• S-duality in N=2 supersymmetric gauge theories
• Multi-Instanton Calculus and Equivariant Cohomology
• Direct Integration of the Topological String
• Recursion relations in CFT and N=2 SYM theory
• The Omega deformed B-model for rigid N=2 theories
• Multi instanton calculus on ALE spaces
• Zamolodchikov asymptotic formula and instanton expansion in N=2 SUSY N_f=2N_c QCD
• On N=2 Supersymmetric QCD with 4 Flavors
• Deformed N=2 theories, generalized recursion relations and S-duality
• Hyperelliptic curves for Supersymmetric Yang-Mills
• Modular anomaly equation, heat kernel and S-duality in N=2 theories
• Instanton Expansions for Mass Deformed N=4 Super Yang-Mills Theories
• $N=2$ Super Yang-Mills and Subgroups of $SL(2,Z)$
• Non-perturbative gauge/gravity correspondence in N=2 theories
• The toroidal block and the genus expansion
• Transformations of Spherical Blocks
• Modular anomaly equations in N=2* theories and their large-N limit
• Exact Electric-Magnetic Duality in N=2 Supersymmetric QCD Theories
• Comparing Instanton Contributions with Exact Results in N=2 Supersymmetric Scale Invariant Theories
• Quantum geometry from the toroidal block
• S-duality and the prepotential in N=2* theories (II): the non-simply laced algebras
• The exact 8d chiral ring from 4d recursion relations
• Non-perturbative studies of N=2 conformal quiver gauge theories
• S-duality and the prepotential in N=2* theories (I): the ADE algebras
• Duality Symmetries for N=2 Supersymmetric QCD with Vanishing beta-Functions
• S-Duality and Global Symmetries in N=2 Supersymmetric Field Theory
• Modular anomaly equations and S-duality in N=2 conformal SQCD
• The Nonperturbative Gauge Coupling of N=2 Supersymmetric Theories
• 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