The Quantum DELL System
High Energy Physics - Theory
2020-04-10 v2 Mathematical Physics
math.MP
Representation Theory
Abstract
We propose quantum Hamiltonians of the double elliptic many-body integrable system (DELL) and study its spectrum. These Hamiltonians are certain elliptic functions of coordinates and momenta. Our results provide quantization of the classical DELL system which was previously found in the string theory literature. The eigenfunctions for the N-body model are instanton partition functions of 6d SU(N) gauge theory with adjoint matter compactified on a torus with a codimension two defect. As a byproduct we discover new family of symmetric orthogonal polynomials which provide an elliptic generalization to Macdonald polynomials.
Cite
@article{arxiv.1906.10354,
title = {The Quantum DELL System},
author = {Peter Koroteev and Shamil Shakirov},
journal= {arXiv preprint arXiv:1906.10354},
year = {2020}
}
Comments
29 pages, 4 figures, comments and references added