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

TL;DR

This paper investigates how $ Z_2^n$-graded Lie superalgebras can serve as new symmetry generators for the $S$-matrix, extending classical symmetry theorems and revealing internal symmetries.

Contribution

It introduces $ Z_2^n$-graded Lie superalgebras as potential symmetry generators of the $S$-matrix, extending existing theorems in quantum field theory.

Findings

A $ Z_2^n$-graded extension of supersymmetry can be a symmetry of the $S$-matrix.

A $ Z_2^n$-graded Lie algebra appears as internal symmetries.

Extensions of Coleman-Mandula and Haag-Lopuszanski-Sohnius theorems are demonstrated.

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.