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

TL;DR

This paper develops a quantum theory for N=2, D=3 superparticles with arbitrary superspin, utilizing Berezin quantization on a supersymmetric phase space and revealing necessary quantum corrections to preserve supersymmetry.

Contribution

It introduces a novel quantization approach combining Berezin and Dirac methods for superparticles with arbitrary superspin, including quantum corrections to supercharges.

Findings

Quantum states realized on supergroup representations.

Quantum corrections are essential for supersymmetry preservation.

Model smoothly contracts to N=1 supersymmetry in BPS limit.

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 $T^\ast({R}^{1,2})\times{L}^{1|2}$, where the inner K\"ahler supermanifold ${L}^{1|2}=OSp(2|2)/[U(1)\times U(1)]=SU(1,1|2)/[U(2|2)\times U(1)]$ provides the particle with superspin degrees of freedom. We find the relationship between Hamiltonian generators of the global Poincar\'e 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.