Quantum geometry from the toroidal block

Abstract

We continue our study of the semi-classical (large central charge) expansion of the toroidal one-point conformal block in the context of the 2d/4d correspondence. We demonstrate that the Seiberg-Witten curve and (epsilon1-deformed) differential emerge naturally in conformal field theory when computing the block via null vector decoupling equations. This framework permits us to derive epsilon1-deformations of the conventional relations governing the prepotential. These enable us to complete the proof of the quasi-modularity of the coefficients of the conformal block in an expansion around large exchanged conformal dimension. We furthermore derive these relations from the semi-classics of exact conformal field theory quantities, such as braiding matrices and the S-move kernel. In the course of our study, we present a new proof of Matone's relation for N=2* theory.

27 pages, 1 figure

References in corpus (32)

• 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
• Solutions Of Four-Dimensional Field Theories Via M Theory
• Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
• Supersymmetric Yang-Mills Systems And Integrable Systems
• Topological Strings and Integrable Hierarchies
• The Refined Topological Vertex
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Instantons and recursion relations in N=2 Susy gauge theory
• Analytic Continuation of Liouville Theory
• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• Quantum Geometry of Refined Topological Strings
• The Omega deformed B-model for rigid N=2 theories
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• Extended Holomorphic Anomaly in Gauge Theory
• Matone's Relation in the Presence of Gravitational Couplings
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Deforming SW curve
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• Deformed N=2 theories, generalized recursion relations and S-duality
• Quantum Painleve-Calogero Correspondence
• On Gauge Theory and Topological String in Nekrasov-Shatashvili Limit
• The toroidal block and the genus expansion
• Transformations of Spherical Blocks
• Multipoint correlation functions in Liouville field theory and minimal Liouville gravity
• S-duality as a beta-deformed Fourier transform
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• Large N techniques for Nekrasov partition functions and AGT conjecture
• The exact 8d chiral ring from 4d recursion relations
• Semiclassical limit of the FZZT Liouville theory

Cited by in corpus (15)

• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• A slow review of the AGT correspondence
• Exact WKB Analysis of N = 2 Gauge Theories
• Non-Perturbative Quantum Geometry II
• Modular and duality properties of surface operators in N=2* gauge theories
• S-duality, triangle groups and modular anomalies in N=2 SQCD
• 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
• 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
• Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2$ theories
• Virasoro blocks and quasimodular forms
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours
• S-move matrix in the NS sector of $N=1$ super Liouville field theory
• Modular properties of surface operators in N=2 SQCD