Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c = 1 Matrix Models
Abstract
We address the nonperturbative structure of topological strings and c=1 matrix models, focusing on understanding the nature of instanton effects alongside with exploring their relation to the largeorder behavior of the 1/N expansion. We consider the Gaussian, Penner and ChernSimons matrix models, together with their holographic duals, the c=1 minimal string at selfdual radius and topological string theory on the resolved conifold. We employ Borel analysis to obtain the exact allloop multiinstanton corrections to the free energies of the aforementioned models, and show that the leading poles in the Borel plane control the largeorder behavior of perturbation theory. We understand the nonperturbative effects in terms of the Schwinger effect and provide a semiclassical picture in terms of eigenvalue tunneling between critical points of the multisheeted matrix model effective potentials. In particular, we relate instantons to Stokes phenomena via a hyperasymptotic analysis, providing a smoothing of the nonperturbative ambiguity. Our predictions for the multiinstanton expansions are confirmed within the transseries setup, which in the doublescaling limit describes nonperturbative corrections to the Toda equation. Finally, we provide a spacetime realization of our nonperturbative corrections in terms of toric Dbrane instantons which, in the doublescaling limit, precisely match Dinstanton contributions to c=1 minimal strings.
 Publication:

Annales Henri Poincaré
 Pub Date:
 June 2010
 DOI:
 10.1007/s0002301000445
 arXiv:
 arXiv:0907.4082
 Bibcode:
 2010AnHP...11..351P
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 71 pages, 14 figures, JHEP3.cls