The quantum DELL system

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 theor...

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Bibliographic Details
Published in:Letters in mathematical physics 2020-05, Vol.110 (5), p.969-999
Main Authors: Koroteev, Peter, Shakirov, Shamil
Format: Article
Language:English
Subjects:
Complex Systems
Eigenvectors
Elliptic cohomology
Elliptic functions
Gauge theory
Geometric representation theory
Geometry
Group Theory and Generalizations
Hamiltonian functions
Instantons
Integrable systems
Mathematical and Computational Physics
Partitions (mathematics)
Physics
Physics and Astronomy
Polynomials
Quantum hydrodynamics
Quantum K-theory
String theory
Supersymmetric gauge theories
Theoretical
Toruses
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Summary: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 by-product, we discover new family of symmetric orthogonal polynomials which provide an elliptic generalization to Macdonald polynomials.
ISSN:0377-9017
1573-0530
1573-0530
DOI:10.1007/s11005-019-01247-y