Supersymmetric V-systems

Abstract

We construct $\mathcal{N}=4$ $D(2,1;\alpha )$ superconformal quantum mechanical system for any configuration of vectors forming a V-system. In the case of a Coxeter root system the bosonic potential of the supersymmetric Hamiltonian is the corresponding generalised Calogero-Moser potential. We also construct supersymmetric generalised trigonometric Calogero-Moser-Sutherland Hamiltonians for some root systems including $B{C}_N$.

31 pages; minor changes

References in corpus (11)

• Supersymmetric Calogero models by gauging
• N=4 superconformal Calogero models
• Integrability of Conformal Blocks I: Calogero-Sutherland Scattering Theory
• N=4 mechanics, WDVV equations and roots
• OSp(4|2) Superconformal Mechanics
• N=4 supersymmetric 3-particles Calogero model
• $\mathcal{N}$-extended supersymmetric Calogero models
• PT-symmetric deformations of Calogero models
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• Supersymmetric many-body Euler-Calogero-Moser model
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Cited by in corpus (3)

• Spinning extensions of $D(2,1;\alpha )$ superconformal mechanics
• WDVV equations and invariant bi-Hamiltonian formalism
• Trigonometric $\vee$-systems and solutions of WDVV equations