Hidden supersymmetry and Berezin quantization of N=2, D=3 spinning superparticles

Abstract

The first quantized theory of N=2, D=3 massive superparticles with arbitrary fixed central charge and (half)integer or fractional superspin is constructed. The quantum states are realized on the fields carrying a finite dimensional, or a unitary infinite dimensional representation of the supergroups OSp(2|2) or SU(1, 1|2). The construction originates from quantization of a classical model of the superparticle we suggest. The physical phase space of the classical superparticle is embedded in a symplectic superspace T * (R 1,2 ) × L 1|2 , where the inner Kähler supermanifold L 1|2 ∼ = OSp(2|2)/[U(1) × U(1)] ∼ = SU(1, 1|2)/[U(2|2) × U(1)] provides the particle with superspin degrees of freedom. We find the relationship between Hamiltonian generators of the global Poincaré supersymmetry and the "internal" SU(1, 1|2) one. Quantization of the superparticle combines the Berezin quantization on L 1|2 and the conventional Dirac quantization with respect to space-time degrees of freedom. Surprisingly, to retain the supersymmetry, quantum corrections are required for the classical N=2 supercharges as compared to the conventional Berezin method. These corrections are derived and the Berezin correspondence principle for L 1|2 underlying their origin is verified. The model admits a smooth contraction to the N=1 supersymmetry in the BPS limit.

Supertwistors and massive particles

“…A (super)twistor formulation of massive 3D particle mechanics in which the (super)twistor variables are alternatives to the usual phase-space was discussed briefly in [17], and here we further develop this formalism. As in the 4D case, we find that the N = 1 massive superparticle action is identical to the N = 2 BPS superparticle action, in agreement with Gorbunov et al [23] (see also [24]). We also obtain the supertwistor form of the N-extended massive 3D "spinning particle".…”