Worldline CPT and massless supermultiplets

TL;DR

This paper investigates the CPT symmetry properties of massless superparticles in 4D Minkowski space, revealing anomalies and degeneracies depending on the number of supersymmetries N, with implications for supermultiplet structures.

Contribution

It demonstrates the anomaly of CPT symmetry for odd N in superparticles and explains the supermultiplet degeneracies for even and odd N using supertwistor formalism.

Findings

CPT symmetry is anomalous for odd N in superparticle models.

CPT self-conjugate supermultiplets exist only for even N.

Supermultiplet size varies with N/2 being odd or even, due to Kramers degeneracy.

Abstract

The action for a massless particle in 4D Minkowski space has a worldline time-reversing symmetry corresponding to CPT invariance of the quantum theory. The analogous symmetry of the N-extended superparticle is shown to be anomalous when N is odd, in the supertwistor formalism this is because a CPT-violating worldline-Chern-Simons term is needed to preserve the chiral U(1) gauge invariance. This accords with the fact that no massless N=1 super-Poincar\'e irrep is CPT-self-conjugate. There is a CPT self-conjugate supermultiplet when N is even, but it has $2^{N+1}$ states when N/2 is odd (e.g. the N=2 hypermultiplet) in contrast to just $2^N$ when N/2 is even (e.g. the N=4 Maxwell supermultiplet). This is shown to follow from a Kramers degeneracy of the superparticle state space when N/2 is odd.