Cubic hypergeometric integrals of motion in affine Gaudin models

Lacroix, Sylvain, Vicedo, Benoit and Young, Charles A. S. (2020) Cubic hypergeometric integrals of motion in affine Gaudin models. Advances in Theoretical and Mathematical Physics, 24 (1). pp. 155-187. ISSN 1095-0761
Copy

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.


picture_as_pdf
CubicHamiltonians_ATMP.pdf
subject
Submitted Version
copyright
Available under Unspecified

View Download

Atom BibTeX OpenURL ContextObject in Span OpenURL ContextObject Dublin Core MPEG-21 DIDL Data Cite XML EndNote HTML Citation METS MODS RIOXX2 XML Reference Manager Refer ASCII Citation
Export

Downloads