# University of Hertfordshire

## Cubic hypergeometric integrals of motion in affine Gaudin models

Research output: Contribution to journalArticle

### Standard

Cubic hypergeometric integrals of motion in affine Gaudin models. / Lacroix, Sylvain; Vicedo, Benoit; Young, Charles A. S.

In: Advances in Theoretical and Mathematical Physics, Vol. 24, No. 1, 22.05.2020, p. 155-187.

Research output: Contribution to journalArticle

### Bibtex

@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 = "World Scientific",
number = "1",

}

### RIS

TY - JOUR

T1 - Cubic hypergeometric integrals of motion in affine Gaudin models

AU - Lacroix, Sylvain

AU - Vicedo, Benoit

AU - Young, Charles A. S.

N1 - © 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.

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

VL - 24

SP - 155

EP - 187

JO - Advances in Theoretical and Mathematical Physics

JF - Advances in Theoretical and Mathematical Physics

SN - 1095-0761

IS - 1

ER -