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- W4367000000 abstract "Topology and generalized symmetries in the $SU(N)/mathbb{Z}_N$ gauge theory are considered in the continuum and the lattice. Starting from the $SU(N)$ gauge theory with the 't~Hooft twisted boundary condition, we give a simpler explanation of the van~Baal's proof on the fractionality of the topological charge. This description is applicable to both continuum and lattice by using the generalized Luscher's construction of topology on the lattice. Thus we can recover the $SU(N)/mathbb{Z}_N$ principal bundle from lattice $SU(N)$ gauge fields being subject to the $mathbb{Z}_N$-relaxed cocycle condition. We explicitly demonstrate the fractional topological charge, and verify an equivalence with other constructions reported recently based on different ideas. Gauging the $mathbb{Z}_N$ $1$-form center symmetry enables lattice gauge theories to couple with the $mathbb{Z}_N$ $2$-form gauge field as a simple lattice integer field, and to reproduce the Kapustin--Seiberg prescription in the continuum limit. Our construction is also applied to analyzing the higher-group structure in the $SU(N)$ gauge theory with the instanton-sum modification." @default.
- W4367000000 created "2023-04-27" @default.
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- W4367000000 date "2023-04-24" @default.
- W4367000000 modified "2023-09-27" @default.
- W4367000000 title "Note on lattice description of generalized symmetries in $SU(N)/mathbb{Z}_N$ gauge theories" @default.
- W4367000000 doi "https://doi.org/10.48550/arxiv.2304.11813" @default.
- W4367000000 hasPublicationYear "2023" @default.
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