The resurgence of instantons: multi-cut Stokes phases and the Painlevé II equation. (English) Zbl 1312.81092
It is believed that non-perturbative phenomena play an important role in quantum field theories describing our world. It is therefore important to understand how such phenomena arise and to develop a formalism to describe them. A natural place to start is to consider simplified models, where various results can be calculated exactly. This is the approach undertaken in this paper. The authors consider non-perturbative phenomena in multi-cut matrix models, which can be thought of as simplest (zero-dimensional) examples of quantum field theories. It turns out that, via the analysis of large \(N\) ’t Hooft solutions of such matrix model, one can quite explicitly study such aspects of non-perturbative phenomena as resurgent transseries and Stokes phases.
Among the others, the authors study models that have important applications in other contexts; for example the triple Penner model computes correlation functions relevant for the AGT conjecture, and solutions of the Painleve II equation describe minimal superstrings. For this reason the results of the paper should be of interest not only to practitioners of matrix models, but also to everyone working on related topics. Nonetheless, a reader should also be warned that the paper is quite long and highly technical. It is certainly recommended to experts in the field, however the newcomers might consult first a couple of earlier papers on these topics.
Among the others, the authors study models that have important applications in other contexts; for example the triple Penner model computes correlation functions relevant for the AGT conjecture, and solutions of the Painleve II equation describe minimal superstrings. For this reason the results of the paper should be of interest not only to practitioners of matrix models, but also to everyone working on related topics. Nonetheless, a reader should also be warned that the paper is quite long and highly technical. It is certainly recommended to experts in the field, however the newcomers might consult first a couple of earlier papers on these topics.
Reviewer: Piotr Sulkowski (Amsterdam)
MSC:
| 81Q80 | Special quantum systems, such as solvable systems |
| 15B52 | Random matrices (algebraic aspects) |
| 81T16 | Nonperturbative methods of renormalization applied to problems in quantum field theory |
| 81T10 | Model quantum field theories |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
Keywords:
non-perturbative phenomena; random matrices; matrix model; large N expansion; resurgent transseriesSoftware:
Wolfram Functions SiteReferences:
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