TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.2.052
TI  - Higher-matter and Landau-Ginzburg theory of higher-group symmetries
PY  - 2025/02/13
UR  - https://www.scipost.org/SciPostPhys.18.2.052
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 2
SP  - 052
A1  - Liu, Ruizhi
AU  - Luo, Ran
AU  - Wang, Yi-Nan
AB  - Higher-matter is defined by higher-representation of a symmetry algebra, such as the $p$-form symmetries, higher-group symmetries or higher-categorical symmetries. In this paper, we focus on the cases of higher-group symmetries, which are formulated in terms of the strictification of weak higher-groups. We systematically investigate higher-matter charged under 2-group symmetries, defined by automorphism 2-representations. Furthermore, we construct a Lagrangian formulation of such higher-matter fields coupled to 2-group gauge fields in the path space of the spacetime manifold. We interpret such model as the Landau-Ginzburg theory for 2-group symmetries, and discuss the spontaneous symmetry breaking (SSB) of 2-group symmetries under this framework. Examples of discrete and continuous 2-groups are discussed. Interestingly, we find that a non-split 2-group symmetry can admit an SSB to a split 2-group symmetry, where the Postnikov class is trivialized. We also briefly discuss the strictification of weak 3-groups, weak 3-group gauge fields and 3-representations in special cases.
ER  -

@Article{10.21468/SciPostPhys.18.2.052,
	title={{Higher-matter and Landau-Ginzburg theory of higher-group symmetries}},
	author={Ruizhi Liu and Ran Luo and Yi-Nan Wang},
	journal={SciPost Phys.},
	volume={18},
	pages={052},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.2.052},
	url={https://scipost.org/10.21468/SciPostPhys.18.2.052},
}