Little Groups of Preon Branes

TL;DR

This paper calculates the little groups for preon branes across dimensions 2 to 11, revealing their structure and invariance properties, with implications for theories involving generalized space-times and brane charges.

Contribution

It provides a comprehensive calculation of little groups for preon branes in various dimensions, including massless and some massive orbits, and explores their invariance properties.

Findings

Little groups for massless preon branes are semidirect products involving translational groups.

At d=9, the subgroup is the exceptional G2 group.

11d Majorana spinor invariants are invariant under d=2+10 Lorentz group.

Abstract

Little groups for preon branes (i.e. configurations of branes with maximal (n-1)/n fraction of survived supersymmetry) for dimensions d=2,3,...,11 are calculated for all massless, and partially for massive orbits. For massless orbits little groups are semidirect product of d-2 translational group $T_{d-2}$ on a subgroup of (SO(d-2) $\times$ R-invariance) group. E.g. at d=9 the subgroup is exceptional $G_2$ group. It is also argued, that 11d Majorana spinor invariants, which distinguish orbits, are actually invariant under d=2+10 Lorentz group. Possible applications of these results include construction of field theories in generalized space-times with brane charges coordinates, different problems of group's representations decompositions, spin-statistics issues.