TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysProc.14.016
TI  - Irreducible representations of $\mathbb{Z}_2^2$-graded supersymmetry algebra and their applications
PY  - 2023/11/23
UR  - https://scipost.org/SciPostPhysProc.14.016
JF  - SciPost Physics Proceedings
JA  - SciPost Phys. Proc.
VL  - 
IS  - 14
SP  - 016
A1  - Aizawa, Naruhiko
AB  - We give a brief review on recent developments of $\mathbb{Z}_2^n$-graded symmetry in physics in which hidden $\mathbb{Z}_2^n$-graded symmetries and $\mathbb{Z}_2^n$-graded extensions of known systems are discussed. This elucidates physical relevance of the $\mathbb{Z}_2^n$-graded algebras. As an example of physically interesting algebra, we take $\mathbb{Z}_2^2$-graded supersymmetry (SUSY) algebras and consider their irreducible representations (irreps). A list of irreps for ${\cal N} = 1, 2$ algebras is presented and as an application of the irreps, $\mathbb{Z}_2^2$-graded SUSY classical actions are constructed.
ER  -

@Article{10.21468/SciPostPhysProc.14.016,
	title={{Irreducible representations of $\mathbb{Z}_2^2$-graded supersymmetry algebra and their applications}},
	author={Naruhiko Aizawa},
	journal={SciPost Phys. Proc.},
	pages={016},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysProc.14.016},
	url={https://scipost.org/10.21468/SciPostPhysProc.14.016},
}