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Phase transitions, double-scaling limit, and topological strings

Caporaso, N, Griguolo, L, Marino, M, Pasquetti, S and Seminara, D (2006) Phase transitions, double-scaling limit, and topological strings Phys.Rev.D, 75.

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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 Painlev\'e 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.

Item Type: Article
Divisions : Surrey research (other units)
Authors :
Caporaso, N
Griguolo, L
Marino, M
Seminara, D
Date : 14 June 2006
DOI : 10.1103/PhysRevD.75.046004
Uncontrolled Keywords : hep-th, hep-th, math.AG
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 12:30
Last Modified : 24 Jan 2020 22:23

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