Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-06-14
Phys.Rev.D75:046004,2007
Physics
High Energy Physics
High Energy Physics - Theory
49 pages, 3 eps figures; section added on non-perturbative proposal and 2d gravity; minor typos corrected
Scientific paper
10.1103/PhysRevD.75.046004
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.
Caporaso Nicola
Griguolo Luca
Marino Marcos
Pasquetti Sara
Seminara Domenico
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