Worldline CPT and massless supermultiplets

Abstract

The action for a massless particle in 4D Minkowski space–time has a worldline-time reversing symmetry corresponding to CPT invariance of the quantum theory. The analogous symmetry of the [Formula: see text]-extended superparticle is shown to be anomalous when [Formula: see text] is odd; in the supertwistor formalism this is because a CPT-violating worldline-Chern–Simons term is needed to preserve the chiral [Formula: see text] gauge invariance. This accords with the fact that no massless [Formula: see text] super-Poincaré irrep is CPT-self-conjugate. There is a CPT self-conjugate supermultiplet when [Formula: see text] is even, but it has [Formula: see text] states when [Formula: see text] is odd (e.g. the [Formula: see text] hypermultiplet) in contrast to just [Formula: see text] when [Formula: see text] is even (e.g. the [Formula: see text] Maxwell supermultiplet). This is shown to follow from a Kramers degeneracy of the superparticle state space when [Formula: see text] is odd.