Supersymmetrization schemes of D=4 Maxwell algebra

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.