N=4 Supersymmetric Multidimensional Quantum Mechanics, Partial SUSY Breaking and Superconformal Quantum Mechanics

TL;DR

This paper constructs multidimensional N=4 supersymmetric quantum mechanics using superfield methods, revealing possibilities for partial supersymmetry breaking and extending previous one-dimensional models to higher dimensions.

Contribution

It introduces a general formalism for multidimensional N=4 SUSY QM, including classical and quantum Lagrangians, and explores partial SUSY breaking scenarios with potential applications.

Findings

Models with various fractions of unbroken supersymmetry exist in multidimensional N=4 SUSY QM.

The formalism generalizes one-dimensional models to higher dimensions.

Partial SUSY breaking can occur with one quarter, one half, or three quarters of unbroken supersymmetries.

Abstract

The multidimensional N=4 supersymmetric quantum mechanics (SUSY QM) is constructed using the superfield approach. As a result, the component form of the classical and quantum Lagrangian and Hamiltonian is obtained. In the considered SUSY QM both classical and quantum N=4 algebras include central charges, and this opens various possibilities for partial supersymmetry breaking. It is shown that quantum mechanical models with one quarter, one half and three quarters of unbroken(broken) supersymmetries can exist in the framework of the multidimensional N=4 SUSY QM, while the one-dimensional N=4 SUSY QM, constructed earlier, admits only one half or total supersymmetry breakdown. We illustrate the constructed general formalism, as well as all possible cases of the partial SUSY breaking taking as an example a direct multidimensional generalization of the one-dimensional N=4 superconformal quantum mechanical model. Some open questions and possible applications of the constructed multidimensional N=4 SUSY QM to the known exactly integrable systems and problems of quantum cosmology are briefly discussed.