Constrained Generalized Supersymmetries
- Centro Brasileiro de Pesquisas Fisicas (Brazil)
We present a classification of admissible types of constraint (hermitian, holomorphic, with reality condition on the bosonic sectors, etc.) for generalized supersymmetries in the presence of complex spinors. A generalized supersymmetry algebra involving n-component real spinors Qa is given by the anticommutators {l_brace}Q{sub a},Q{sub b}{r_brace} = Z{sub ab} where the matrix Z appearing in the r.h.s. is the most general symmetric matrix. A complex generalized supersymmetry algebra is expressed in terms of complex spinors Qa and their complex conjugate Q* a. The most general (with a saturated r.h.s.) algebra is in this case given by {l_brace}Q{sub a},Q{sub b}{r_brace} P{sub ab}{l_brace}Q*{sub a}, Q*{sub b}{r_brace} = P*{sub ab}{l_brace}Q{sub a},Q*{sub b}{r_brace} = R{sub ab} where the matrix Pab is symmetric, while Rab is hermitian. The bosonic right hand side can be expressed in terms of the rank-k totally antisymmetric tensors P{sub ab} {sigma}k(C{gamma}{sub [{mu}}{sub 1...{mu}}{sub k]}){sub ab}P{sup [{mu}{sup 1...{mu}{sup k}]}.The decomposition in terms of anti-symmetric tensors for any space-time up to dimension D = 13 is presented. Real type, complex type, and quaternionic type space-times are classified. Any restriction on the saturated bosonic generators that allows all possible combinations of these tensors is in principle admissible by a Lorenz-covariant requirement. We investigate division algebra constraints and their influence on physical models. High spin theory models are presented as examples of the applications of such models.
- OSTI ID:
- 20719565
- Journal Information:
- AIP Conference Proceedings, Vol. 795, Issue 1; Conference: 2. IUPAP international conference on women in physics, Rio de Janeiro (Brazil), 23-25 May 2005; Other Information: DOI: 10.1063/1.2128369; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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