Transmutation of a trans-series: the Gross-Witten-Wadia phase transition
Abstract 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...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-11-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP11(2017)054 |
| _version_ | 1818990764544229376 |
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| author | Anees Ahmed Gerald V. Dunne |
| author_facet | Anees Ahmed Gerald V. Dunne |
| author_sort | Anees Ahmed |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-12-20T19:59:33Z |
| format | Article |
| id | doaj.art-6ace4d1b051f435891a6041526d3ac68 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-20T19:59:33Z |
| publishDate | 2017-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-6ace4d1b051f435891a6041526d3ac682022-12-21T19:28:05ZengSpringerOpenJournal of High Energy Physics1029-84792017-11-0120171115210.1007/JHEP11(2017)054Transmutation of a trans-series: the Gross-Witten-Wadia phase transitionAnees Ahmed0Gerald V. Dunne1Department of Physics, University of ConnecticutDepartment of Physics, University of ConnecticutAbstract 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.http://link.springer.com/article/10.1007/JHEP11(2017)054Nonperturbative Effects1/N ExpansionMatrix Models |
| spellingShingle | Anees Ahmed Gerald V. Dunne Transmutation of a trans-series: the Gross-Witten-Wadia phase transition Journal of High Energy Physics Nonperturbative Effects 1/N Expansion Matrix Models |
| title | Transmutation of a trans-series: the Gross-Witten-Wadia phase transition |
| title_full | Transmutation of a trans-series: the Gross-Witten-Wadia phase transition |
| title_fullStr | Transmutation of a trans-series: the Gross-Witten-Wadia phase transition |
| title_full_unstemmed | Transmutation of a trans-series: the Gross-Witten-Wadia phase transition |
| title_short | Transmutation of a trans-series: the Gross-Witten-Wadia phase transition |
| title_sort | transmutation of a trans series the gross witten wadia phase transition |
| topic | Nonperturbative Effects 1/N Expansion Matrix Models |
| url | http://link.springer.com/article/10.1007/JHEP11(2017)054 |
| work_keys_str_mv | AT aneesahmed transmutationofatransseriesthegrosswittenwadiaphasetransition AT geraldvdunne transmutationofatransseriesthegrosswittenwadiaphasetransition |