MS Seminar (Mathematics - String Theory)

Speaker: Yuya Tanizaki (RIKEN BNL Research Center)
Title: Cheshire Cat Resurgence and Quasi-Exact Solvability
Date: Tue, Dec 06, 2016, 13:15 - 14:30
Place: Seminar Room A
Abstract: Perturbation theory is a useful technique to understand interacting quantum systems. However, if one considers this technique seriously, one typically finds the factorial growth of the perturbative coefficients and the result diverges. People have developed the "resurgence theory" to understand and overcome this difficulty by relating it with nonperturbative corrections.
In this talk, we first briefly review the asymptotic nature of perturbation theory and what is the resurgence relation. After that, we apply this idea to certain quantum mechanical systems, called Quasi-Exactly Solvable (QES) systems. There is a puzzle for this system in its semiclassical analysis: This system does not suffer from the nonperturbative corrections, however there is a 2-instanton solution giving a nonperturbative correction. We solve this puzzle by using the resurgence relation (Cheshire Cat Resurgence) to show the exact cancellation of such nonperturbative correction with another correction coming from complex classical solutions.
Furthermore, we extend this idea to other systems without QES to predict nonperturbative energy shift.