Harmonic N=2 Mechanics

TL;DR

This paper explores a special class of N=2 superconformal many-body quantum mechanics models characterized by harmonic functions, highlighting their classification, properties, and examples across various dimensions.

Contribution

It introduces a new class of models with harmonic potentials, classifies them using symmetry constraints, and discusses their quantized central charge and examples in multiple dimensions.

Findings

Models with absent bosonic potential classified by harmonic functions.

Central charge is naturally quantized in these models.

Examples provided for identical particles in any dimension.

Abstract

N=2 superconformal many-body quantum mechanics in arbitrary dimensions is governed by a single scalar prepotential which determines the bosonic potential and the boson-fermion couplings. We present a special class of such models, for which the bosonic potential is absent. They are classified by homogeneous harmonic functions subject to physical symmetry requirements, such as translation, rotation and permutation invariance. The central charge is naturally quantized. We provide some examples for systems of identical particles in any dimension.