|
This article is cited in 7 scientific papers (total in 7 papers)
The Endless Beta Integrals
Gor A. Sarkissianabc, Vyacheslav P. Spiridonovba a Laboratory of Theoretical Physics, JINR, Dubna, 141980, Russia
b St. Petersburg Department of the Steklov Mathematical Institute of Russian Academy
of Sciences, Fontanka 27, St. Petersburg, 191023 Russia
c Department of Physics, Yerevan State University, Yerevan, Armenia
Abstract:
We consider a special degeneration limit $\omega_1\to - \omega_2$ (or $b\to {\rm i}$ in the context of $2d$ Liouville quantum field theory) for the most general univariate hyperbolic beta integral. This limit is also applied to the most general hyperbolic analogue of the Euler–Gauss hypergeometric function and its $W(E_7)$ group of symmetry transformations. Resulting functions are identified as hypergeometric functions over the field of complex numbers related to the $\mathrm{SL}(2,\mathbb{C})$ group. A new similar nontrivial hypergeometric degeneration of the Faddeev modular quantum dilogarithm (or hyperbolic gamma function) is discovered in the limit $\omega_1\to \omega_2$ (or $b\to 1$).
Keywords:
elliptic hypergeometric functions, complex gamma function, beta integrals, star-triangle relation.
Received: May 5, 2020; in final form July 24, 2020; Published online August 5, 2020
Citation:
Gor A. Sarkissian, Vyacheslav P. Spiridonov, “The Endless Beta Integrals”, SIGMA, 16 (2020), 074, 21 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1611 https://www.mathnet.ru/eng/sigma/v16/p74
|
Statistics & downloads: |
Abstract page: | 121 | Full-text PDF : | 36 | References: | 22 |
|