Unexpected Features of Supersymmetry with Central Charges

Abstract

In the paper under review, the authors show that some specific graded Lie superalgebras could induce specific quartic extensions of Lie algebras. Such construction is then applied to show that it can be associated naturally a quartic extension of the Poincaré algebra to the standard N = 2 supersymmetric extensions with central charges. This construction shows that the central charges play an important role because they constitute the essential ingredient to introduce the notion of a hidden quartic symmetry. It follows that massive invariant N = 2 Lagrangians are also invariant with respect to these hidden symmetries. The authors finally conclude that the quartic extensions obtained for such method give raise to a hierarchy of representations emerging from the standard representation of the corresponding supersymmetric theory. It could be interesting to study the case for N > 2.