The toroidal block and the genus expansion

Abstract

We study the correspondence between four-dimensional supersymmetric gauge theories and two-dimensional conformal field theories in the case of N=2* gauge theory. We emphasize the genus expansion on the gauge theory side, as obtained via geometric engineering from the topological string. This point of view uncovers modular properties of the one-point conformal block on a torus with complexified intermediate momenta: in the large intermediate weight limit, it is a power series whose coefficients are quasi-modular forms. The all-genus viewpoint that the conformal field theory approach lends to the topological string yields insight into the analytic structure of the topological string partition function in the field theory limit.

36 pages

References in corpus (6)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• The Refined Topological Vertex
• Extended Holomorphic Anomaly in Gauge Theory
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Loop operators and S-duality from curves on Riemann surfaces
• On Gauge Theory and Topological String in Nekrasov-Shatashvili Limit

Cited by in corpus (32)

• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• Refined BPS invariants of 6d SCFTs from anomalies and modularity
• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• Deformed N=2 theories, generalized recursion relations and S-duality
• Modular anomaly equation, heat kernel and S-duality in N=2 theories
• Holographic interpretation of 1-point toroidal block in the semiclassical limit
• Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equation
• A slow review of the AGT correspondence
• Transformations of Spherical Blocks
• Exact WKB Analysis of N = 2 Gauge Theories
• Modular anomaly equations in N=2* theories and their large-N limit
• Classical irregular block, N=2 pure gauge theory and Mathieu equation
• Holographic duals of large-c torus conformal blocks
• Transmutation of a Trans-series: The Gross-Witten-Wadia Phase Transition
• Quantum geometry from the toroidal block
• Modular and duality properties of surface operators in N=2* gauge theories
• S-duality, triangle groups and modular anomalies in N=2 SQCD
• Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations
• Monodromy methods for torus conformal blocks and entanglement entropy at large central charge
• Non-perturbative studies of N=2 conformal quiver gauge theories
• On the large $\Omega$-deformations in the Nekrasov-Shatashvili limit of $\mathcal{N}=2^{\ast }$ SYM
• Resurgence, Painleve Equations and Conformal Blocks
• Chiral observables and S-duality in N = 2* U(N) gauge theories
• Recurrence relations for the ${\mathcal{W}}_3$ conformal blocks and $\mathcal{N}=2$ SYM partition functions
• Exact partition functions for the $\Omega$-deformed $\mathcal{N}=2^{\ast }$ $SU(2)$ gauge theory
• Semiclassical torus blocks in the t-channel
• Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2$ theories
• Virasoro blocks and quasimodular forms
• Hyperbolic deformation of the strip-equation and the accessory parameters for the torus
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours
• Classical conformal blocks, Coulomb gas integrals and Richardson-Gaudin models
• Modular properties of surface operators in N=2 SQCD