Constrained generalized supersymmetries and superparticles with tensorial central charges. A classification

TL;DR

This paper classifies types of constraints in generalized supersymmetries with complex spinors, explores dual formulations, and constructs superparticle models with tensorial central charges, including higher-spin particle towers.

Contribution

It provides a systematic classification of constrained generalized supersymmetries and constructs superparticle models with tensorial central charges, extending previous models to complex spinors.

Findings

Classified admissible constraints for complex and real spinor supersymmetries.

Identified dual formulations of constrained supersymmetries.

Constructed superparticle models with tensorial central charges and higher-spin towers.

Abstract

We classify the admissible types of constraint (hermitian, holomorphic, with reality conditions on the bosonic sectors, etc.) for generalized supersymmetries in the presence of complex spinors. We further point out which constrained generalized supersymmetries admit a dual formulation. For both real and complex spinors generalized supersymmetries are constructed and classified as dimensional reductions of supersymmetries from {\em oxidized} space-times (i.e. the maximal space-times associated to $n$-component Clifford irreps). We apply these results to sistematically construct a class of models describing superparticles in presence of bosonic tensorial central charges, deriving the consistency conditions for the existence of the action, as well as the constrained equations of motion. Examples of these models (which, in their twistorial formulation, describe towers of higher-spin particles) were first introduced by Rudychev and Sezgin (for real spinors) and later by Bandos and Lukierski (for complex spinors).