Quantum mechanics of superparticle with 1/4 supersymmetry breaking

TL;DR

This paper investigates the quantum mechanics of a superparticle in four dimensions that preserves a quarter of the supersymmetry, revealing a rich supermultiplet structure and connections to differential forms despite Lorentz symmetry breaking.

Contribution

It provides a detailed Hamiltonian and quantum analysis of a superparticle with partial supersymmetry breaking, uncovering its supermultiplet structure and vacuum properties.

Findings

Supermultiplet contains three N=2 multiplets with 8 complex components.

States correspond to de Rham complex of p-forms on a 3D subspace.

Non-trivial vacua are exact harmonic forms.

Abstract

We study quantum mechanics of a massive superparticle in d=4 which preserves 1/4 of the target space supersymmetry with eight supercharges, and so corresponds to the partial breaking N=8 down to N=2. Its worldline action contains a Wess-Zumino term, explicitly breaks d=4 Lorentz symmetry and exhibits one complex fermionic kappa-symmetry. We perform the Hamiltonian analysis of the model and quantize it in two different ways, with gauge-fixed kappa-symmetry and in the Gupta-Bleuler formalism. Both approaches give rise to the same supermultiplet structure of the space of states. It contains three irreducible N=2 multiplets with the total number of (4+4) complex on-shell components. These states prove to be in one-to-one correspondence with the de Rham complex of p-forms on a three-dimensional subspace of the target x-manifold. We analyze the vacuum structure of the model and find that the non-trivial vacua are given by the exact harmonic one- and two-forms. Despite the explicit breaking of the d=4 Lorentz symmetry in the fermionic sector, the d=4 mass-shell condition is still valid in the model.