Unitary matrix models and random partitions: Universality and multi-criticality
Abstract The generating functions for the gauge theory observables are often represented in terms of the unitary matrix integrals. In this work, the perturbative and non-perturbative aspects of the generic multi-critical unitary matrix models are studied by adopting the integrable operator formalism...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
SpringerOpen
2021-07-01
|
Series: | Journal of High Energy Physics |
Subjects: | |
Online Access: | https://doi.org/10.1007/JHEP07(2021)100 |
id |
doaj-e014d39ad45347ebaf074fbc46156363 |
---|---|
record_format |
Article |
spelling |
doaj-e014d39ad45347ebaf074fbc461563632021-07-18T11:50:28ZengSpringerOpenJournal of High Energy Physics1029-84792021-07-012021714810.1007/JHEP07(2021)100Unitary matrix models and random partitions: Universality and multi-criticalityTaro Kimura0Ali Zahabi1Institut de Mathématiques de Bourgogne, Université Bourgogne Franche-ComtéInstitut de Mathématiques de Bourgogne, Université Bourgogne Franche-ComtéAbstract The generating functions for the gauge theory observables are often represented in terms of the unitary matrix integrals. In this work, the perturbative and non-perturbative aspects of the generic multi-critical unitary matrix models are studied by adopting the integrable operator formalism, and the multi-critical generalization of the Tracy-Widom distribution in the context of random partitions. We obtain the universal results for the multi-critical model in the weak and strong coupling phases. The free energy of the instanton sector in the weak coupling regime, and the genus expansion of the free energy in the strong coupling regime are explicitly computed and the universal multi-critical phase structure of the model is explored. Finally, we apply our results in concrete examples of supersymmetric indices of gauge theories in the large N limit.https://doi.org/10.1007/JHEP07(2021)1001/N ExpansionIntegrable HierarchiesMatrix ModelsSupersymmetric Gauge Theory |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Taro Kimura Ali Zahabi |
spellingShingle |
Taro Kimura Ali Zahabi Unitary matrix models and random partitions: Universality and multi-criticality Journal of High Energy Physics 1/N Expansion Integrable Hierarchies Matrix Models Supersymmetric Gauge Theory |
author_facet |
Taro Kimura Ali Zahabi |
author_sort |
Taro Kimura |
title |
Unitary matrix models and random partitions: Universality and multi-criticality |
title_short |
Unitary matrix models and random partitions: Universality and multi-criticality |
title_full |
Unitary matrix models and random partitions: Universality and multi-criticality |
title_fullStr |
Unitary matrix models and random partitions: Universality and multi-criticality |
title_full_unstemmed |
Unitary matrix models and random partitions: Universality and multi-criticality |
title_sort |
unitary matrix models and random partitions: universality and multi-criticality |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2021-07-01 |
description |
Abstract The generating functions for the gauge theory observables are often represented in terms of the unitary matrix integrals. In this work, the perturbative and non-perturbative aspects of the generic multi-critical unitary matrix models are studied by adopting the integrable operator formalism, and the multi-critical generalization of the Tracy-Widom distribution in the context of random partitions. We obtain the universal results for the multi-critical model in the weak and strong coupling phases. The free energy of the instanton sector in the weak coupling regime, and the genus expansion of the free energy in the strong coupling regime are explicitly computed and the universal multi-critical phase structure of the model is explored. Finally, we apply our results in concrete examples of supersymmetric indices of gauge theories in the large N limit. |
topic |
1/N Expansion Integrable Hierarchies Matrix Models Supersymmetric Gauge Theory |
url |
https://doi.org/10.1007/JHEP07(2021)100 |
work_keys_str_mv |
AT tarokimura unitarymatrixmodelsandrandompartitionsuniversalityandmulticriticality AT alizahabi unitarymatrixmodelsandrandompartitionsuniversalityandmulticriticality |
_version_ |
1721295840927023104 |