Supersymmetrization Schemes of D=4 Maxwell Algebra

TL;DR

This paper explores various supersymmetrizations of the Maxwell algebra in four dimensions, classifying multiple superextensions derived through algebra contractions, and discusses potential applications of these superalgebras.

Contribution

It systematically constructs and classifies N-extended Maxwell superalgebras in D=4 via contractions of real superalgebras, revealing multiple new superextensions and internal symmetry structures.

Findings

Multiple N-extended Maxwell superalgebras identified

Different superextensions correspond to various contractions of real superalgebras

Potential applications in theoretical physics discussed

Abstract

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