# University of Hertfordshire

## Cubic hypergeometric integrals of motion in affine Gaudin models

Research output: Contribution to journalArticlepeer-review

### Documents

Original language English 155-187 33 Advances in Theoretical and Mathematical Physics 24 1 https://doi.org/10.4310/ATMP.2020.v24.n1.a5 Published - 22 May 2020

### 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.

### Notes

© 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.

ID: 17049682