Quantum mechanics of a superparticle with 1/4 supersymmetry breaking

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 $N=\stackrel{\ensuremath{\rightarrow}}{8}N=2.$ Its worldline action contains a Wess-Zumino term, explicitly breaks $d=4$ Lorentz symmetry and exhibits one complex fermionic $\ensuremath{\kappa}$ symmetry. We perform the Hamiltonian analysis of the model and quantize it in two different ways: with gauge-fixed $\ensuremath{\kappa}$ 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 nontrivial vacua are given by the exact harmonic one- and two-forms. Despite the explicit breaking of $d=4$ Lorentz symmetry in the fermionic sector, the $d=4$ mass-shell condition is still valid in the model.