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arXiv · hep-th/0606120

Phase transitions, double-scaling limit, and topological strings

Nicola Caporaso·Luca Griguolo·Marcos Marino·Sara Pasquetti·Domenico Seminara
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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.

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Nicola Caporaso, Luca Griguolo, Marcos Marino, Sara Pasquetti, Domenico Seminara. 2007-01-10. Phase transitions, double-scaling limit, and topological strings. https://doi.org/10.1103/physrevd.75.046004

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