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

Ren Ito, Akio Nago

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.

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

Abstract

In this paper, we explore the -graded Lie (super)algebras as novel possible generators of symmetries of -matrix. As the results, we demonstrate that a -graded extension of the supersymmetric algebra can be a symmetry of -matrix. Furthermore, it turns out that a -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 -matrix.
Paper Structure (10 sections, 4 theorems, 45 equations, 1 table)

This paper contains 10 sections, 4 theorems, 45 equations, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. $\mathbb{Z}_2^n$-graded Lie superalgebra
  4. Coleman-Mandula theorem
  5. Haag-Ł opuszański-Sohnius theorem
  6. Novel possible generators of the $S$-matrix
  7. Possible $\mathbb{Z}_2^2$-graded generators of symmetries
  8. Possible $\mathbb{Z}_2^n$-graded generators of symmetries
  9. $\mathbb{Z}_2^n$-Graded internal symmetries
  10. Concluding remarks

Key Result

Theorem 1

There exits the unique $\mathbb{Z}_2^2$-graded extension of supersymmetric algebra which is given by the $\mathbb{Z}_2^2$-graded LSA $\langle P_\mu, Z^{(1)}_{KL}, \bar{Z}^{(1)}_{KL}, Z^{(2)}_{KL}, \bar{Z}^{(2)}_{KL}, Z^{11}_{KL}, \bar{Z}^{11}_{KL}, Q_{\alpha\,K}^{01}, \bar{Q}_{\dot{\alpha}\,K}^{01},

Theorems & Definitions (9)

  • Definition 1
  • Definition 2
  • Theorem 1
  • Theorem 2
  • Definition 3
  • Theorem 3
  • proof
  • Definition 4
  • Theorem 4