D=(0|2) Dirac--Maxwell--Einstein Theory as a Way for Describing Supersymmetric Quartions

TL;DR

This paper develops a supersymmetric theoretical framework for describing quartions, particles with fractional spin, using a superfield action in a (0|2) dimensional model that relates to effective (2+1)-dimensional space-time.

Contribution

It introduces a novel supersymmetric equations of motion and superfield action for quartions, linking fractional spin particles to a (0|2) supersymmetric model with gravitational and gauge interactions.

Findings

Formulation of supersymmetric equations for quartions.

Construction of a superfield action in (0|2) dimensions.

Representation of quartions in an effective (2+1)-dimensional space-time.

Abstract

Drawing an analogy with the Dirac theory of fermions interacting with electromagnetic and gravitational field we write down supersymmetric equations of motion and construct a superfield action for particles with spin 1/4 and 3/4 (quartions), where the role of quartion momentum in effective (2+1)--dimensional space-time is played by an abelian gauge superfield propagating in a basic two-dimensional Grassmann-odd space with a cosmological constant showing itself as the quartion mass. So, the (0|2) (0 even and 2 odd) dimensional model of quartions interacting with the gauge and gravitational field manifests itself as an effective (2+1)-dimensional supersymmetric theory of free quartions.