The supersymmetric Ruijsenaars-Schneider model

Abstract

An integrable supersymmetric generalization of the trigonometric Ruijsenaars-Schneider model is presented whose symmetry algebra includes the super Poincaré algebra. Moreover, its Hamiltonian is showed to be diagonalized by the recently introduced Macdonald superpolynomials. Somewhat surprisingly, the consistency of the scalar product forces the discreteness of the Hilbert space.

v1: 11 pages, 1 figure. v2: new format, 5 pages, short section added at the end of the article addressing the problem of consistency of the scalar product (e.g., positivity of the weight functions and the normalization of the ground state wave function). To appear in Physical Review Letters

References in corpus (2)

• Fractional Quantum Hall States and Jack Polynomials
• Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $\alpha$

Cited by in corpus (7)

• On $\mathcal{N}=2$ supersymmetric Ruijsenaars-Schneider models
• Schur Superpolynomials: Combinatorial Definition and Pieri Rule
• Macdonald polynomials for super-partitions
• N=2 supersymmetric extensions of relativistic Toda lattice
• From Jack to Double Jack Polynomials via the Supersymmetric Bridge
• Symmetric functions in superspace: a compendium of results and open problems (including a SageMath worksheet)
• Pieri rules for the Jack polynomials in superspace and the 6-vertex model