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- W3101043345 abstract "A bstract We study the change in the resurgent asymptotic properties of a trans-series in two parameters, a coupling g 2 and a gauge index N , as a system passes through a large N phase transition, using the universal example of the Gross-Witten-Wadia third-order phase transition in the unitary matrix model. This transition is well-studied in the immediate vicinity of the transition point, where it is characterized by a double-scaling limit Painlevé II equation, and also away from the transition point using the pre-string difference equation. Here we 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 Painlevé III equation. This mapping provides a simple method to generate trans-series expansions in all parameter regimes, and to study their transmutation as the parameters are varied. For example, at any finite N the weak coupling expansion is divergent, with a non-perturbative trans-series completion; on the other hand, the strong coupling expansion is convergent, and yet there is still a non-perturbative trans-series completion. We show how the different instanton terms ‘condense’ at the transition point to match with the double-scaling limit trans-series. We 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." @default.
- W3101043345 created "2020-11-23" @default.
- W3101043345 creator A5050103242 @default.
- W3101043345 creator A5062556177 @default.
- W3101043345 date "2017-11-01" @default.
- W3101043345 modified "2023-09-25" @default.
- W3101043345 title "Transmutation of a trans-series: the Gross-Witten-Wadia phase transition" @default.
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- W3101043345 doi "https://doi.org/10.1007/jhep11(2017)054" @default.
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