Non-Perturbative Topological Strings And Conformal Blocks

Abstract

We give a non-perturbative completion of a class of closed topological string theories in terms of building blocks of dual open strings. In the specific case where the open string is given by a matrix model these blocks correspond to a choice of integration contour. We then apply this definition to the AGT setup where the dual matrix model has logarithmic potential and is conjecturally equivalent to Liouville conformal field theory. By studying the natural contours of these matrix integrals and their monodromy properties, we propose a precise map between topological string blocks and Liouville conformal blocks. Remarkably, this description makes use of the light-cone diagrams of closed string field theory, where the critical points of the matrix potential correspond to string interaction points.

36 pages

References in corpus (7)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• The Refined Topological Vertex
• Affine SL(2) conformal blocks from 4d gauge theories
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Seiberg-Witten theory, matrix model and AGT relation
• Seiberg-Witten curve via generalized matrix model

Cited by in corpus (20)

• Nonperturbative aspects of ABJM theory
• Holomorphic Blocks in Three Dimensions
• Quantum Geometry of Refined Topological Strings
• M5-branes, toric diagrams and gauge theory duality
• The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painleve II Equation
• Vertices, Vortices & Interacting Surface Operators
• The toroidal block and the genus expansion
• A slow review of the AGT correspondence
• Parafermionic Liouville field theory and instantons on ALE spaces
• Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings
• Orientifolds and the Refined Topological String
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• Refined Black Hole Ensembles and Topological Strings
• Non-perturbative studies of N=2 conformal quiver gauge theories
• AdS2/CFT1, Whittaker vector and Wheeler-De Witt equation
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Trinion Conformal Blocks from Topological strings
• Chiral observables and S-duality in N = 2* U(N) gauge theories
• Notes on 3-point functions of A_{N-1} Toda theory and AGT-W relation for SU(N) quiver
• Penner Type Ensemble for Gauge Theories Revisited