The Quantum DELL System

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.

29 pages, 4 figures, comments and references added

References in corpus (5)

• Defects and Quantum Seiberg-Witten Geometry
• Seiberg-Witten curves and double-elliptic integrable systems
• D-type fiber-base duality
• New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential
• Modular properties of 6d (DELL) systems

Cited by in corpus (19)

• Duality in elliptic Ruijsenaars system and elliptic symmetric functions
• Intersecting Defects and Supergroup Gauge Theory
• On complete solution of the quantum Dell system
• Elliptic Quantum Curves of Class ${\mathcal{S}}_k$
• Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
• Dualities in quantum integrable many-body systems and integrable probabilities -- I
• On the status of DELL systems
• On Dimensional Transmutation in 1+1D Quantum Hydrodynamics
• Characteristic determinant and Manakov triple for the double elliptic integrable system
• Double Inozemtsev Limits of the Quantum DELL System
• Ground state wavefunctions of elliptic relativistic integrable Hamiltonians
• The deformed Inozemtsev spin chain
• Non-stationary difference equation for q-Virasoro conformal blocks
• On Cherednik and Nazarov-Sklyanin large N limit construction for integrable many-body systems with elliptic dependence on momenta
• Elliptic triad
• Diamond of triads
• Elliptic Ruijsenaars difference operators, symmetric polynomials, and Wess-Zumino-Witten fusion rings
• A basic triad in Macdonald theory
• 5D AGT conjecture for circular quivers