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

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Cited by in corpus (16)

• Ruijsenaars-Schneider three-body models with N=2 supersymmetry
• On $\mathcal{N}=2$ supersymmetric Ruijsenaars-Schneider models
• Schur Superpolynomials: Combinatorial Definition and Pieri Rule
• Trigonometric and elliptic Ruijsenaars-Schneider systems on the complex projective space
• Macdonald polynomials for super-partitions
• N=2 supersymmetric extensions of relativistic Toda lattice
• Supersymmetric polynomials and algebro-combinatorial duality
• From Jack to Double Jack Polynomials via the Supersymmetric Bridge
• Supersymmetric generalization of q-deformed long-range spin chains of Haldane-Shastry type and trigonometric GL(N|M) solution of associative Yang-Baxter equation
• S-move matrix in the NS sector of $N=1$ super Liouville field theory
• Pieri rules for the Jack polynomials in superspace and the 6-vertex model
• Symmetric functions in superspace: a compendium of results and open problems (including a SageMath worksheet)
• Integrable many-body systems of Calogero-Ruijsenaars type
• Elliptic Ruijsenaars difference operators, symmetric polynomials, and Wess-Zumino-Witten fusion rings
• Bernstein operators and super-Schur functions: combinatorial aspects
• Super-Hamiltonians for super-Macdonald polynomials