The Hyperbolic Asymptotics of Elliptic Hypergeometric Integrals Arising in Supersymmetric Gauge Theory
The purpose of this article is to demonstrate that i) the framework of elliptic hypergeometric integrals (EHIs) can be extended by input from supersymmetric gauge theory, and ii) analyzing the hyperbolic limit of the EHIs in the extended framework leads to a rich structure containing sharp mathemati...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209529 |
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| Cite this: | The Hyperbolic Asymptotics of Elliptic Hypergeometric Integrals Arising in Supersymmetric Gauge Theory / A.A. Ardehali // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 50 назв. — англ. |
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Ardehali, A.A. 2025-11-24T10:42:40Z 2018 The Hyperbolic Asymptotics of Elliptic Hypergeometric Integrals Arising in Supersymmetric Gauge Theory / A.A. Ardehali // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 50 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33D67; 33E05; 41A60; 81T13; 81T60 arXiv: 1712.09933 https://nasplib.isofts.kiev.ua/handle/123456789/209529 https://doi.org/10.3842/SIGMA.2018.043 The purpose of this article is to demonstrate that i) the framework of elliptic hypergeometric integrals (EHIs) can be extended by input from supersymmetric gauge theory, and ii) analyzing the hyperbolic limit of the EHIs in the extended framework leads to a rich structure containing sharp mathematical problems of interest to supersymmetric quantum field theorists. Both of the above items have already been discussed in the theoretical physics literature. Item i was demonstrated by Dolan and Osborn in 2008. Item ii was discussed in the present author's Ph.D. Thesis in 2016, wherein crucial elements were borrowed from the 2006 work of Rains on the hyperbolic limit of certain classes of EHIs. This article contains a concise review of these developments, along with minor refinements and clarifying remarks, written mainly for mathematicians interested in EHIs. In particular, we work with a representation-theoretic definition of a supersymmetric gauge theory, so that readers without any background in gauge theory - but familiar with the representation theory of semi-simple Lie algebras - can follow the discussion. I would like to thank P. Miller and E. Rains for discussions on the mathematical side, as well as G. Festuccia, J.T. Liu, and P. Szepietowski for discussions on the physical side of the subject. I am also grateful to the anonymous referees, whose informative comments and constructive feedback on a draft of this manuscript have contributed significantly to its subsequent improvement. This work was supported in part by the National Elites Foundation of Iran. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Hyperbolic Asymptotics of Elliptic Hypergeometric Integrals Arising in Supersymmetric Gauge Theory Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
The Hyperbolic Asymptotics of Elliptic Hypergeometric Integrals Arising in Supersymmetric Gauge Theory |
| spellingShingle |
The Hyperbolic Asymptotics of Elliptic Hypergeometric Integrals Arising in Supersymmetric Gauge Theory Ardehali, A.A. |
| title_short |
The Hyperbolic Asymptotics of Elliptic Hypergeometric Integrals Arising in Supersymmetric Gauge Theory |
| title_full |
The Hyperbolic Asymptotics of Elliptic Hypergeometric Integrals Arising in Supersymmetric Gauge Theory |
| title_fullStr |
The Hyperbolic Asymptotics of Elliptic Hypergeometric Integrals Arising in Supersymmetric Gauge Theory |
| title_full_unstemmed |
The Hyperbolic Asymptotics of Elliptic Hypergeometric Integrals Arising in Supersymmetric Gauge Theory |
| title_sort |
hyperbolic asymptotics of elliptic hypergeometric integrals arising in supersymmetric gauge theory |
| author |
Ardehali, A.A. |
| author_facet |
Ardehali, A.A. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
The purpose of this article is to demonstrate that i) the framework of elliptic hypergeometric integrals (EHIs) can be extended by input from supersymmetric gauge theory, and ii) analyzing the hyperbolic limit of the EHIs in the extended framework leads to a rich structure containing sharp mathematical problems of interest to supersymmetric quantum field theorists. Both of the above items have already been discussed in the theoretical physics literature. Item i was demonstrated by Dolan and Osborn in 2008. Item ii was discussed in the present author's Ph.D. Thesis in 2016, wherein crucial elements were borrowed from the 2006 work of Rains on the hyperbolic limit of certain classes of EHIs. This article contains a concise review of these developments, along with minor refinements and clarifying remarks, written mainly for mathematicians interested in EHIs. In particular, we work with a representation-theoretic definition of a supersymmetric gauge theory, so that readers without any background in gauge theory - but familiar with the representation theory of semi-simple Lie algebras - can follow the discussion.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209529 |
| citation_txt |
The Hyperbolic Asymptotics of Elliptic Hypergeometric Integrals Arising in Supersymmetric Gauge Theory / A.A. Ardehali // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 50 назв. — англ. |
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2025-12-07T14:44:27Z |
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2025-12-07T14:44:27Z |
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1850886081222803456 |