Phase transitions, double-scaling limit, and topological strings

Abstract

Topological strings on Calabi--Yau manifolds are known to undergo phase transitions at small distances. We study this issue in the case of perturbative topological strings on local Calabi--Yau threefolds given by a bundle over a two-sphere. This theory can be regarded as a q--deformation of Hurwitz theory, and it has a conjectural nonperturbative description in terms of q--deformed 2d Yang--Mills theory. We solve the planar model and find a phase transition at small radius in the universality class of 2d gravity. We give strong evidence that there is a double--scaled theory at the critical point whose all genus free energy is governed by the Painlevé I equation. We compare the critical behavior of the perturbative theory to the critical behavior of its nonperturbative description, which belongs to the universality class of 2d supergravity. We also give evidence for a new open/closed duality relating these Calabi--Yau backgrounds to open strings with framing.

49 pages, 3 eps figures; section added on non-perturbative proposal and 2d gravity; minor typos corrected

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Cited by in corpus (32)

• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• Open string amplitudes and large order behavior in topological string theory
• Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c=1 Matrix Models
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• Vertices, Vortices & Interacting Surface Operators
• Seiberg-Witten theory and matrix models
• Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory
• Toda hierarchies and their applications
• Hurwitz numbers, matrix models and enumerative geometry
• The local Gromov-Witten theory of CP^1 and integrable hierarchies
• Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings
• D-branes as a Bubbling Calabi-Yau
• Open topological strings and integrable hierarchies: Remodeling the A-model
• Exact results for topological strings on resolved Y(p,q) singularities
• Matrix models for 2* theories
• Wall Crossing As Seen By Matrix Models
• Black Holes in Type IIA String on Calabi-Yau Threefolds with Affine ADE Geometries and q-Deformed 2d Quiver Gauge Theories
• Local mirror symmetry of curves: Yukawa couplings and genus 1
• Modified melting crystal model and Ablowitz-Ladik hierarchy
• $T\bar{T}$-deformed 2D Yang-Mills at large N: collective field theory and phase transitions
• Mirror symmetry for extended affine Weyl groups
• Integrable structure of melting crystal model with two q-parameters
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• Matrix models and stochastic growth in Donaldson-Thomas theory
• Extended $5d$ Seiberg-Witten Theory and Melting Crystal
• Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles
• Integrable structure of modified melting crystal model
• A Note on q-Deformed Two-Dimensional Yang-Mills and Open Topological Strings
• On equivariant mirror symmetry for local P^2
• Enumerative geometry of surfaces and topological strings
• Stringy Instanton Counting and Topological Strings
• A Unitary Matrix Model for $q$-deformed Plancherel Growth