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 -extended superparticle is shown to be anomalous when 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 = 1 super-Poincaré irrep is CPT-self-conjugate. There is a CPT self-conjugate supermultiplet when is even, but it has 2+1 states when 1 2 is odd (e.g. the = 2 hypermultiplet) in contrast to just 2 when 1 2 is even (e.g. the = 4 Maxwell supermultiplet). This is shown to follow from a Kramers degeneracy of the superparticle state space when 1 2 is odd.
- time reversal
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Nuclear and High Energy Physics
- Astronomy and Astrophysics