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The Hilbert series of N=1 SO(N c) and Sp(N c) SQCD, Painlevé VI and integrable systems
Basor E.1; Chen Y.2,3; Mekareeya N.4
2012-07-21
Source PublicationNuclear Physics B
ISSN05503213
Volume860Issue:3Pages:421-463
Abstract

We present a novel approach for computing the Hilbert series of 4d N=1 supersymmetric QCD with SO(N ) and Sp(N ) gauge groups. It is shown that such Hilbert series can be recast in terms of determinants of Hankel matrices. With the aid of results from random matrix theory, such Hankel determinants can be evaluated both exactly and asymptotically. Several new results on Hilbert series for general numbers of colours and flavours are thus obtained in this paper. We show that the Hilbert series give rise to families of rational solutions, with palindromic numerators, to the Painlevé VI equations. Due to the presence of such Painlevé equations, there exist integrable Hamiltonian systems that describe the moduli spaces of SO(N ) and Sp(N ) SQCD. To each system, we explicitly state the corresponding Hamiltonian and family of elliptic curves. It turns out that such elliptic curves take the same form as the Seiberg-Witten curves for 4d N=2 SU(2) gauge theory with 4 flavours. © 2012 Elsevier B.V.

DOIhttps://doi.org/10.1016/j.nuclphysb.2012.02.018
URLView the original
Indexed BySCI
Language英语
WOS Research AreaPhysics
WOS SubjectPhysics, Particles & Fields
WOS IDWOS:000302989300004
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Cited Times [WOS]:8   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorMekareeya N.
Affiliation1.American Institute of Mathematics, 360 Portage Avenue, Palo Alto, CA 9430, USA
2.Department of Mathematics, Imperial College London, 180 Queenʼs Gates, London SW7 2BZ, UK
3.Department of Mathematics, Faculty of Science and Technology, University of Macau, Av. Padre Tomás Pereira, Taipa, Macau, China
4.Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805 München, Germany
Recommended Citation
GB/T 7714
Basor E.,Chen Y.,Mekareeya N.. The Hilbert series of N=1 SO(N c) and Sp(N c) SQCD, Painlevé VI and integrable systems[J]. Nuclear Physics B,2012,860(3):421-463.
APA Basor E.,Chen Y.,&Mekareeya N..(2012).The Hilbert series of N=1 SO(N c) and Sp(N c) SQCD, Painlevé VI and integrable systems.Nuclear Physics B,860(3),421-463.
MLA Basor E.,et al."The Hilbert series of N=1 SO(N c) and Sp(N c) SQCD, Painlevé VI and integrable systems".Nuclear Physics B 860.3(2012):421-463.
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