Twistor form of massive 6D superparticle

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.

Section: (S)pl Tensors For Dimensions D = 3 4supporting

confidence: 81%

Section: Jhep06(2017)151supporting

confidence: 76%

“…From this fact, and the expression (1.5) for the Casimir C 2 , it follows that 8) where the last equality is a consequence of the identity…”

Section: Jhep06(2017)151mentioning

confidence: 89%

“…This expression is polynomial in the Noether charges, so Y is indeed a PL vector, as shown in [8] using SU * (4)-spinor notation. We may use it to construct the quartic Poincaré Casimir…”

Section: The 6d Quartic Casimirmentioning

confidence: 96%

“…UsingP instead of P we may construct the PL tensor For d = 6 this is equivalent to a relation found in [8] using SU * (4) notation. 9 The left and right inverse are equal, even for K = H.…”

Section: Spin-shell Constraints and The Quadratic Casimirmentioning

confidence: 99%

See 3 more Smart Citations

Pauli-Lubanski, supertwistors, and the superspinning particle

Arvanitakis

Mezincescu

Townsend

2017

Twistor description of spinning particles in AdS

Arvanitakis

Barns-Graham

Townsend

2018

Abstract:The two-twistor formulation of particle mechanics in D-dimensional anti-de Sitter space for D = 4, 5, 7, which linearises invariance under the AdS isometry group Sp(4; K) for K = R, C, H, is generalized to the massless N -extended "spinning particle". The twistor variables are gauge invariant with respect to the initial N local worldline supersymmetries; this simplifies aspects of the quantum theory such as implications of global gauge anomalies. We also give details of the two-supertwistor form of the superparticle, in particular the massive superparticle on AdS 5 .

Manifestly covariant worldline actions from coadjoint orbits. Part I. Generalities and vectorial descriptions

Basile,

Joung,

2024

We derive manifestly covariant actions of spinning particles starting from coadjoint orbits of isometry groups, by using Hamiltonian reductions. We show that the defining conditions of a classical Lie group can be treated as Hamiltonian constraints which generate the coadjoint orbits of another, dual, Lie group. In case of (inhomogeneous) orthogonal groups, the dual groups are (centrally-extended inhomogeneous) symplectic groups. This defines a symplectic dual pair correspondence between the coadjoint orbits of the isometry group and those of the dual Lie group, whose quantum version is the reductive dual pair correspondence à la Howe. We show explicitly how various particle species arise from the classification of coadjoint orbits of Poincaré and (A)dS symmetry. In the Poincaré case, we recover the data of the Wigner classification, which includes continuous spin particles, (spinning) tachyons and null particles with vanishing momenta, besides the usual massive and massless spinning particles. In (A)dS case, our classification results are not only consistent with the pattern of the corresponding unitary irreducible representations observed in the literature, but also contain novel information. In dS, we find the presence of partially massless spinning particles, but continuous spin particles, spinning tachyons and null particles are absent. The AdS case shows the largest diversity of particle species. It has all particles species of Poincaré symmetry except for the null particle, but allows in addition various exotic entities such as one parameter extension of continuous particles and conformal particles living on the boundary of AdS. Notably, we also find a large class of particles living in “bitemporal” AdS space, including ones where mass and spin play an interchanged role. We also discuss the relative inclusion structure of the corresponding orbits.