Many-particle mechanics with D(2,1;alpha) superconformal symmetry

Abstract

We overcome the barrier of constructing N=4 superconformal models in one space dimension for more than three particles. The D(2,1;alpha) superalgebra of our systems is realized on the coordinates and momenta of the particles, their superpartners and one complex pair of harmonic variables. The models are determined by two prepotentials, F and U, which must obey the WDVV and a Killing-type equation plus homogeneity conditions. We investigate permutation-symmetric solutions, with and without translation invariance. Models based on deformed A_n and BCD_n root systems are constructed for any value of alpha, and exceptional F_n-type and super root systems admit solutions as well. Translation-invariant mechanics occurs for any number of particles at alpha=-1/2 (osp(4|2) invariance as a degenerate limit) and for four particles at arbitrary alpha (three series).

1+12 pages, no figures; v2: two refs added, typos corrected, version published in JHEP; v3: minor correction to (3.8) & (3.10)

References in corpus (12)

• Supersymmetric Calogero models by gauging
• N=4 superconformal Calogero models
• New D(2,1;alpha) Mechanics with Spin Variables
• N=4 mechanics, WDVV equations and roots
• N=4 supersymmetric 3-particles Calogero model
• Potentials in N=4 superconformal mechanics
• Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems
• N=4 Multi-Particle Mechanics, WDVV Equation and Roots
• On the geometry of V-systems
• A new class of solutions to the WDVV equation
• Trigonometric Solutions of the WDVV Equations from Root Systems
• Dual multiplets in N=4 superconformal mechanics

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