Superparticles, p-form coordinates and the BPS condition

Abstract

A model for n superparticles in (d − n, n) dimensions is studied. The target space supersymmetry involves a product of n momentum generators, and the action has n(n + 1)/2 local bosonic symmetries and n local fermionic symmetries. The precise relation between the symmetries presented here and those existing in the literature is explained. A new model is proposed for superparticles in arbitrary dimensions where coordinates are associated with all the p-form charges occuring in the superalgebra. The model naturally gives rise to the BPS condition for the charges.

Conformal higher spin symmetries of 4D massless supermultiplets andosp(L,2M)invariant equations in generalized (super)space

“…The twistor reformulation was initiated in [73,74] and further developed in [75,76,77,47,60,78,79]. The idea that additional (often called central charge) coordinates have to be introduced to extend the twistor approach beyond four dimensions was exploited in [47,48,49,50,80,81].…”

“…Some ideas on a possible structure of alternative to Minkowski space-times have appeared both in the field-theoretical [38,30,39,40,41,42,43,44,45,46] and world particle dynamics [47,48,49,50] contexts. In particular, important algebraic and geometric insights most relevant to the subject of this paper were elaborated by Fronsdal in the pioneering work [30].…”

A Clifford Algebra Realization of Supersymmetry and its Polyvector Extension in Clifford Spaces

“…Appl. Cliff ord Algebras symmetries and supertwistor dynamics by [8,9,16]. For this reason we believe we ought to explore how to build the novel Polyvector Supersymmetic structures in Clifford Spaces.…”

“…Other Hermitian versus holomorphic complex and quaternionic generalized supertranslations ( " supersymmetries" ) of M -theory were classified by [8]. The classification of the family of symmetric matrices (Cγ μ1μ2...μn ) αβ is what restricts the type of terms that appear in the {Q α , Q β } anticommutator and depends on the number of space time dimensions D, the signatures (s, t) and the rank n. A table of the allowed values of D, s, t, n can be found in [16] .…”

“…The relevant terms are once again {Q α , Q β }, [Q α , Q β ] and which are given in terms of suitable products of gamma matrices which furnish an overall symmetric and anti-symmetric matrix in the α, β indices, respectively. The classification of the family of symmetric and antisymmetric matrices (Cγ i1i2...im ) αβ , (Cγ j1j2...jn ) αβ depends on the number of space time dimensions D, the signatures (s, t) and the ranks m, n. A table of the allowed values of D, s, t, m furnishing a symmetric matrix can be found in [16] . One just needs to look at the table for the allowed values of D, s, t, n furnishing an antisymmetric matrix, in addition to the symmetric cases.…”