University of Connecticut

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PhD Dissertation Defense

Monday, May 7, 2018
1:00pm – 3:00pm

Storrs Campus
P121

Anees Ahmed, Department of Physics, University of Connecticut

Resurgence and Large N: the Gross-Witten-Wadia model

I present a detailed study of parametric resurgence in the Gross-Witten-Wadia unitary model. I show how trans-series expansions in different sectors transmute into each other as they pass through the large N phase transition. This transition is well-studied in the immediate vicinity of the transition point. Here I present a complementary analysis of the transition at all coupling and all finite N, in terms of a differential equation, using the explicit Tracy-Widom mapping of the Gross-Witten-Wadia partition function to a solution of a Painleve III equation. This mapping provides a simple method to generate trans-series expansions in all parameter regimes. A surprising result is uncovered: the strong coupling expansion is convergent and yet there is a non-perturbative trans-series completion. I also define a uniform large N strong-coupling expansion (a non-linear analogue of uniform WKB), which is much more precise than the conventional large N expansion through the transition region, and apply it to the evaluation of Wilson loops and the Beta function.

Contact:

Prof. G. Dunne

Physics Department (primary), UConn Master Calendar

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