Geometric transitions, double scaling limits and gauge theories

Abstract

In the present work certain features of the Penner model, such its enumerative meaning and its relation to the Chern-Simons theory on the 3-sphere, are reviewed. Also, some features related to geometric transitions at the level of the observables are discussed. In this setup, the non commutative five dimensional U(1) Nekrasov partition function is interpreted as a limiting case of a mean value of the Ooguri-Vafa operator for a Chern-Simons model, which is dual to the A-model on a toric Calabi-Yau with $h_{1,1}=1$ and $h_{2,1}=2$. We work out a B-model interpretation of this identification explicitly by considering this model on the corresponding mirror geometries.