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 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-Poincaré irrep is CPT-self-conjugate. There is a CPT self-conjugate supermultiplet when 𝒩 is even, but it has 2𝒩+1 states when 12𝒩 is odd (e.g. the 𝒩=2 hypermultiplet) in contrast to just 2𝒩 when 12𝒩 is even (e.g. the 𝒩=4 Maxwell supermultiplet). This is shown to follow from a Kramers degeneracy of the superparticle state space when 12𝒩 is odd.
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