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The Quantum DELL System
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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.
Forward citations
Cited by 3 Pith papers
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Surface Defects in $A$-type Little String Theories
The authors give a combinatorial partition function for A-type little string theories with a full-type surface defect and argue that two NS-limit regularizations are both regular due to a recursive pole-cancellation identity.
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Elliptic triad
The paper argues that the Macdonald triad admits elliptic deformations, but the defining linear equations for elliptic Baker-Akhiezer functions remain ambiguous except at m=1.
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