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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• Fine structure of Hagedorn transitions
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Cited by in corpus (11)

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• Hurwitz numbers, matrix models and enumerative geometry
• Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings
• D-branes as a Bubbling Calabi-Yau
• Matrix models for 2* theories
• Black Holes in Type IIA String on Calabi-Yau Threefolds with Affine ADE Geometries and q-Deformed 2d Quiver Gauge Theories
• Integrable structure of melting crystal model with two q-parameters
• Extended $5d$ Seiberg-Witten Theory and Melting Crystal
• Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles