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Эта публикация цитируется в 14 научных статьях (всего в 14 статьях)
Elliptic Hypergeometric Sum/Integral Transformations and Supersymmetric Lens Index
Andrew P. Kelsa, Masahito Yamazakib a Institute of Physics, University of Tokyo, Komaba, Tokyo 153-8902, Japan
b Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Chiba 277-8583, Japan
Аннотация:
We prove a pair of transformation formulas for multivariate elliptic hypergeometric sum\slash integrals associated to the $A_n$ and $BC_n$ root systems, generalising the formulas previously obtained by Rains. The sum/integrals are expressed in terms of the lens elliptic gamma function, a generalisation of the elliptic gamma function that depends on an additional integer variable, as well as a complex variable and two elliptic nomes. As an application of our results, we prove an equality between $S^1\times S^3/\mathbb{Z}_r$ supersymmetric indices, for a pair of four-dimensional $\mathcal{N}=1$ supersymmetric gauge theories related by Seiberg duality, with gauge groups ${\rm SU}(n+1)$ and ${\rm Sp}(2n)$. This provides one of the most elaborate checks of the Seiberg duality known to date. As another application of the $A_n$ integral, we prove a star-star relation for a two-dimensional integrable lattice model of statistical mechanics, previously given by the second author.
Ключевые слова:
elliptic hypergeometric; elliptic gamma; supersymmetric; Seiberg duality; integrable; exactly solvable; Yang–Baxter; star-star.
Поступила: 24 апреля 2017 г.; в окончательном варианте 2 февраля 2018 г.; опубликована 16 февраля 2018 г.
Образец цитирования:
Andrew P. Kels, Masahito Yamazaki, “Elliptic Hypergeometric Sum/Integral Transformations and Supersymmetric Lens Index”, SIGMA, 14 (2018), 013, 29 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1312 https://www.mathnet.ru/rus/sigma/v14/p13
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