Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
- PDF / 615,834 Bytes
- 29 Pages / 595.276 x 841.89 pts (A4) Page_size
- 35 Downloads / 213 Views
Springer
Received: June 9, 2020 Accepted: July 23, 2020 Published: August 28, 2020
Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
a
Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan b KMI, Nagoya University, Nagoya, 464-8602, Japan c Theory Department, Lebedev Physics Institute, Leninsky pr., 53, Moscow 119991, Russia d ITEP, Bol. Cheremushkinskaya, 25, Moscow 117218, Russia e Institute for Information Transmission Problems, Bol. Karetny, 19 (1), Moscow 127994, Russia f MIPT, Institutsky per., 9, Dolgoprudny, Moscow Region 141701, Russia
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: As a development of [1], we note that the ordinary Shiraishi functions have an insufficient number of parameters to describe generic eigenfunctions of double elliptic system (Dell). The lacking parameter can be provided by substituting elliptic instead of the ordinary Gamma functions in the coefficients of the series. These new functions (ELS-functions) are conjectured to be functions governed by compactified DIM networks which can simultaneously play the three roles: solutions to non-stationary Dell equations, Dell conformal blocks with the degenerate field (surface operator) insertion, and the corresponding instanton sums in 6d SUSY gauge theories with adjoint matter. We describe the basics of the corresponding construction and make further conjectures about the various limits and dualities which need to be checked to make a precise statement about the Dell description by double-periodic network models with DIM symmetry. We also demonstrate that the ELS-functions provide symmetric polynomials, which are an elliptic generalization of Macdonald ones, and compute the generation function of the elliptic genera of the affine Laumon spaces. In the particular U(1) case, we find an explicit plethystic formula for the 6d partition function, which is a non-trivial elliptic generalization of the (q, t) NekrasovOkounkov formula from 5d. Keywords: Integrable Hierarchies, Supersymmetric Gauge Theory, Topological Strings, Duality in Gauge Field Theories ArXiv ePrint: 2005.10563
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP08(2020)150
JHEP08(2020)150
Hidetoshi Awata,a Hiroaki Kanno,a,b Andrei Mironovc,d,e and Alexei Morozovf,d,e
Contents 1
2 ELS-function
3
3 Symmetric polynomials from ELS-functions
6
4 Duality properties
7
5 Shiraishi function and the compactification of DIM network
8
6 ELS-function and the double compactified DIM network
9
6d (Q , Λ; q, t) 7 Summing up ZU(1) i
13
8 Elliptic genus of the affine Laumon space
16
9 Conjecture and various limits
21
10 Conclusion
23
1
Introduction
Nekrasov’s extension [2, 3] of Seiberg-Witten theory [4, 5] describes instanton sums (LMNS integrals [6, 7]) in the Ω-background deformed supersymmetric Yang-Mills theories. Like Seiberg-Witten theory itself [8, 9], this extension can be encoded in terms of the theory of int
Data Loading...
