Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
| dc.creator | Marino, Marcos | |
| dc.date | 2008-05-20 | |
| dc.date | 2008-10-14 | |
| dc.date.accessioned | 2026-07-07T12:27:22Z | |
| dc.date.available | 2026-07-07T12:27:22Z | |
| dc.description | We develop techniques to compute multi-instanton corrections to the 1/N expansion in matrix models described by orthogonal polynomials. These techniques are based on finding trans-series solutions, i.e. formal solutions with exponentially small corrections, to the recursion relations characterizing the free energy. We illustrate this method in the Hermitian, quartic matrix model, and we provide a detailed description of the instanton corrections in the Gross-Witten-Wadia (GWW) unitary matrix model. Moreover, we use Borel resummation techniques and results from the theory of resurgent functions to relate the formal multi-instanton series to the nonperturbative definition of the matrix model. We study this relation in the case of the GWW model and its double-scaling limit, providing in this way a nice illustration of various mechanisms connecting the resummation of perturbative series to nonperturbative results, like the cancellation of nonperturbative ambiguities. Finally, we argue that trans-series solutions are also relevant in the context of topological string theory. In particular, we point out that in topological string models with both a matrix model and a large N gauge theory description, the nonperturbative, holographic definition involves a sum over the multi-instanton sectors of the matrix model | |
| dc.description | 50 pages, 12 figures, comments and references added, small corrections | |
| dc.identifier | https://arxiv.org/abs/0805.3033 | |
| dc.identifier | http://arxiv.org/abs/0805.3033 | |
| dc.identifier | JHEP 0812:114,2008 | |
| dc.identifier | doi:10.1088/1126-6708/2008/12/114 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215186 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | High Energy Physics - Lattice | |
| dc.subject | Mathematical Physics | |
| dc.title | Nonperturbative effects and nonperturbative definitions in matrix models and topological strings | |
| dc.type | text |