Phase transitions, topological strings and 2d gravity
Fri, Oct. 13th 2006, 11:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
Topological strings in Calabi--Yau manifolds undergo phase transitions at small distances that signal the onset of quantum geometry. In most models the universality class of the transition is the c=1 string at selfdual radius. In this talk I analyze these transitions for topological strings on bundles over a sphere, which are described by a q--deformation of Hurwitz theory. Their critical behavior turns out to be in the universality class of pure 2d gravity, and one can define a double--scaled theory at the critical point governed by the Painleve I equation. These theories have moreover a conjectural nonperturbative description in terms of q--deformed Yang--Mills theory, which exhibit a generalized Douglas--Kazakov transition. I speculate on the implications of this description for the nonperturbative completion of pure 2d gravity.