Novel possible symmetries of $S$-matrix generated by ${\mathbb{Z}}_2^n$-graded Lie superalgebras

Abstract

In this paper, we explore the ${\mathbb{Z}}_2^n$-graded Lie (super)algebras as novel possible generators of symmetries of $S$-matrix. As the results, we demonstrate that a ${\mathbb{Z}}_2^n$-graded extension of the supersymmetric algebra can be a symmetry of $S$-matrix. Furthermore, it turns out that a ${\mathbb{Z}}_2^n$-graded Lie algebra appears as internal symmetries. They are natural extensions of Coleman-Mandula theorem and Haag-Lopszanski-Sohnius theorem, which are the no-go theorems for generators of symmetries of $S$-matrix.

17 pages