Pauli-Lubanski, supertwistors, and the superspinning particle

Abstract

We present a novel construction of the super-Pauli-Lubanski pseudo-vector for 4D supersymmetry and show how it arises naturally from the spin-shell constraints in the supertwistor formulation of superparticle dynamics. We illustrate this result in the context of a simple classical action for a "superspinning particle" of superspin 1/2. We then use an Sl(2; K)-spinor formalism for K = R, C, H to unify our 4D results with previous results for 3D and 6D.

Chiral strings, topological branes, and a generalised Weyl-invariance

“…where here and henceforth = d p+1 σ unless noted. Notice that both S 0 and S 1 are real because we are using the atypical complex conjugation convention (also used in [4,15]) that sends ψ 1 ψ 2 →ψ 1ψ2 if ψ 1 , ψ 2 are fermionic. From the fact the master action is linear in antifields we see that the gauge transformations close off-shell and that they are irreducible.…”

“…The matrix Ω is the standard 4 × 4 symplectic matrix, and the dagger denotes K-hermitian conjugation. We refer to [4,15] for more details on this division-algebra notation.…”

Twistor description of spinning particles in AdS

“…Notice that Ψ 2 is anti-hermitian, since we are using a convention such that hermitian conjugation does not change the order of anticommuting factors. For the K = C case we have 37) and the K = R case is found by setting ψ = 0. A special feature of these cases is that Ψ 2 is traceless.…”

“…A significant feature of that action (which carries over to the AdS D case) is that the twistor variables, and the new anticommuting variables required for non-zero spin, are all gauge invariant with respect to the original local worldline supersymmetry. The only remaining gauge-invariances other than time-reparametrization invariance are the local SO(N) (for N > 1) and those generated by the O(2; K) "spin-shell" constraints (which determine the Pauli-Lubanski 3-form [37]). Here we rederive these results using the Sl(2; K) and Sp(4; K) notation to express them in a uniform way for d = 3, 4, 6, and we take this opportunity to explain details of the new notation.…”

Worldline CPT and massless supermultiplets

“…which imposes a limitation to massless particles. We have recently generalized this construction so that it also applies to massive particles [17], but the massless case will suffice here. In this case one finds that Z m = HP m for the Poisson bracket realisation of the super-Poincaré algebra, where H is a "classical superhelicity".…”