Supersymmetrization schemes of D=4 Maxwell algebra

• Published in: Physics letters. B Vol. 707; no. 2; pp. 292 - 297
• Main Authors: Kamimura, Kiyoshi, Lukierski, Jerzy
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 20.01.2012; Elsevier
• Subjects: Algebra; Contraction of algebra; Elementary particles; Enlargement; Exact sciences and technology; Generators; Maxwell algebra; Nuclear physics; Physics; Recall; Supersymmetry; Symmetry; The physics of elementary particles and fields; Supersymmetry; Contraction of algebra; Maxwell algebra; Superalgebra; Internal symmetry; SL(2,C) group
• ISSN: 0370-2693; 1873-2445
• DOI: 10.1016/j.physletb.2011.12.037

The Maxwell algebra, an enlargement of Poincaré algebra by Abelian tensorial generators, can be obtained in arbitrary dimension D by the suitable contraction of O(D−1,1)⊕O(D−1,2) (Lorentz algebra ⊕ AdS algebra). We recall that in D=4 the Lorentz algebra O(3,1) is described by the realification SpR(2|C) of complex algebra Sp(2|C)≃Sl(2|C) and O(3,2)≃Sp(4). We study various D=4N-extended Maxwell superalgebras obtained by the contractions of real superalgebras OSpR(2N−k;2|C)⊕OSp(k;4) (k=0,1,2,…,2N); (extended Lorentz superalgebra ⊕ extended AdS superalgebra). If N=1 (k=0,1,2) one arrives at three different versions of simple Maxwell superalgebra. For any fixed N we get 2N different superextensions of Maxwell algebra with n-extended Poincaré superalgebras (1⩽n⩽N) and the internal symmetry sectors obtained by suitable contractions of the real algebra OR(2N−k|C)⊕O(k). Finally the comments on possible applications of Maxwell superalgebras are presented.