Superspinors and Graded Lorentz Groups in Three, Four and Five Dimensions

Abstract

Three superalgebras osp(1; 2;

On the Maxwell supergravity and flat limit in 2 + 1 dimensions

“…The most natural minimal supersymmetric extension of the Lorentz algebra in three spacetime dimensions is spanned by Lorentz generators M a and Majorana fermionic generators Q α (α = 1, 2) [63]. The (anti-)commutation relations read…”

Superconformal structures on the three-sphere

“…where e = (e α β ) is the rigid supersymmetric one-form (4.46). 12 As a result, the super-interval is…”

On schizosymmetric superfields and $sl(2/1, \Bbb{ C})_\Bbb{R}$ supersymmetry

“…From the super-Lorentz representations established in §3, namely Φ I ≃ (8, 0)+(0, 8), and Φ II ≃ (4, 4), there is a natural identification of type II schizofields as 'gauge potential-like' (containing a vector potential A µ as one component), and type I schizofields as 'field strength-like' (containing an antisymmetric tensor F µν as one component), respectively. A scenario for Lagrangian construction would then be to model a generalised gauge potential as a Grassmann-odd, type II schizofield Φ II ≡ A, say, and to introduce an 'exterior' operator of the form D = Γ µ ∂ x µ for suitable odd Γ µ , for example Γ µ = θ µ or Γ µ = γ µ (see (3)). Local gauge invariance would then be implemented through F = DA + A ⋆ A (including possible nonabelian extensions) † † .…”

“…Apart from antecedents in general works on supersymmetry and superfields (see references in [1]), work related to the present approach to superfields is that of [2], which also develops superfields over vector Grassmann coordinates (especially in d ≥ 5 dimensions) extended to local symmetries. In connection with generalised 'graded Lorentz' supersymmetries, the paper [3] should be noted. Finally, although having the use of vector Grassmann coordinates in common, studies of supersymmetric quantum mechanics and the index theorem (see for example [4]) and related spinning particle models appear to be different from the present schizosymmetric superfields.…”