Cubic hypergeometric integrals of motion in affine Gaudin models

Sylvain Lacroix; Benoit Vicedo; Charles A. S. Young

doi:10.4310/ATMP.2020.v24.n1.a5

Cubic hypergeometric integrals of motion in affine Gaudin models

Sylvain Lacroix, Benoit Vicedo, Charles A. S. Young

Mathematics and Theoretical Physics

Research output: Contribution to journal › Article › peer-review

80 Downloads (Pure)

Abstract

We construct cubic Hamiltonians for quantum Gaudin models of affine types $\hat{\mathfrak{sl}}_M$. They are given by hypergeometric integrals of a form we recently conjectured in arXiv:1804.01480. We prove that they commute amongst themselves and with the quadratic Hamiltonians. We prove that their vacuum eigenvalues, and their eigenvalues for one Bethe root, are given by certain hypergeometric functions on a space of affine opers.

Original language	English
Pages (from-to)	155-187
Number of pages	33
Journal	Advances in Theoretical and Mathematical Physics
Volume	24
Issue number	1
DOIs	https://doi.org/10.4310/ATMP.2020.v24.n1.a5
Publication status	Published - 22 May 2020

Keywords

math.QA
hep-th

Access to Document

10.4310/ATMP.2020.v24.n1.a5Licence: Unspecified

CubicHamiltonians_ATMP
© 2020 International Press of Boston, Inc. This is the accepted manuscript version of an article which has been published in final form at https://dx.doi.org/10.4310/ATMP.2020.v24.n1.a5.
Accepted author manuscript, 406 KBLicence: Unspecified

Cite this

@article{ee3bd6be27604a00bfe4f8d6ebf66620,

title = "Cubic hypergeometric integrals of motion in affine Gaudin models",

abstract = "We construct cubic Hamiltonians for quantum Gaudin models of affine types $\hat{\mathfrak{sl}}_M$. They are given by hypergeometric integrals of a form we recently conjectured in arXiv:1804.01480. We prove that they commute amongst themselves and with the quadratic Hamiltonians. We prove that their vacuum eigenvalues, and their eigenvalues for one Bethe root, are given by certain hypergeometric functions on a space of affine opers. ",

keywords = "math.QA, hep-th",

author = "Sylvain Lacroix and Benoit Vicedo and Young, {Charles A. S.}",

note = "{\textcopyright} 2020 International Press of Boston, Inc. This is the accepted manuscript version of an article which has been published in final form at https://dx.doi.org/10.4310/ATMP.2020.v24.n1.a5.",

year = "2020",

month = may,

day = "22",

doi = "10.4310/ATMP.2020.v24.n1.a5",

language = "English",

volume = "24",

pages = "155--187",

journal = "Advances in Theoretical and Mathematical Physics",

issn = "1095-0761",

publisher = "International Press of Boston, Inc.",

number = "1",

}

TY - JOUR

T1 - Cubic hypergeometric integrals of motion in affine Gaudin models

AU - Lacroix, Sylvain

AU - Vicedo, Benoit

AU - Young, Charles A. S.

PY - 2020/5/22

Y1 - 2020/5/22

N2 - We construct cubic Hamiltonians for quantum Gaudin models of affine types $\hat{\mathfrak{sl}}_M$. They are given by hypergeometric integrals of a form we recently conjectured in arXiv:1804.01480. We prove that they commute amongst themselves and with the quadratic Hamiltonians. We prove that their vacuum eigenvalues, and their eigenvalues for one Bethe root, are given by certain hypergeometric functions on a space of affine opers.

AB - We construct cubic Hamiltonians for quantum Gaudin models of affine types $\hat{\mathfrak{sl}}_M$. They are given by hypergeometric integrals of a form we recently conjectured in arXiv:1804.01480. We prove that they commute amongst themselves and with the quadratic Hamiltonians. We prove that their vacuum eigenvalues, and their eigenvalues for one Bethe root, are given by certain hypergeometric functions on a space of affine opers.

KW - math.QA

KW - hep-th

U2 - 10.4310/ATMP.2020.v24.n1.a5

DO - 10.4310/ATMP.2020.v24.n1.a5

M3 - Article

SN - 1095-0761

VL - 24

SP - 155

EP - 187

JO - Advances in Theoretical and Mathematical Physics

JF - Advances in Theoretical and Mathematical Physics

IS - 1

ER -

Cubic hypergeometric integrals of motion in affine Gaudin models

Abstract

Keywords

Access to Document

Fingerprint

Cite this