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• W2951623434 abstract "We study 3d and 4d systems with a one-form global symmetry, explore their consequences, and analyze their gauging. For simplicity, we focus on $mathbb{Z}_N$ one-form symmetries. A 3d topological quantum field theory (TQFT) $mathcal{T}$ with such a symmetry has $N$ special lines that generate it. The braiding of these lines and their spins are characterized by a single integer $p$ modulo $2N$. Surprisingly, if $gcd(N,p)=1$ the TQFT factorizes $mathcal{T}=mathcal{T}'otimes mathcal{A}^{N,p}$. Here $mathcal{T}'$ is a decoupled TQFT, whose lines are neutral under the global symmetry and $mathcal{A}^{N,p}$ is a minimal TQFT with the $mathbb{Z}_N$ one-form symmetry of label $p$. The parameter $p$ labels the obstruction to gauging the $mathbb{Z}_N$ one-form symmetry; i.e. it characterizes the 't Hooft anomaly of the global symmetry. When $p=0$ mod $2N$, the symmetry can be gauged. Otherwise, it cannot be gauged unless we couple the system to a 4d bulk with gauge fields extended to the bulk. This understanding allows us to consider $SU(N)$ and $PSU(N)$ 4d gauge theories. Their dynamics is gapped and it is associated with confinement and oblique confinement -- probe quarks are confined. In the $PSU(N)$ theory the low-energy theory can include a discrete gauge theory. We will study the behavior of the theory with a space-dependent $theta$-parameter, which leads to interfaces. Typically, the theory on the interface is not confining. Furthermore, the liberated probe quarks are anyons on the interface. The $PSU(N)$ theory is obtained by gauging the $mathbb{Z}_N$ one-form symmetry of the $SU(N)$ theory. Our understanding of the symmetries in 3d TQFTs allows us to describe the interface in the $PSU(N)$ theory." @default.
• W2951623434 created "2019-06-27" @default.
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• W2951623434 date "2019-03-29" @default.
• W2951623434 modified "2023-10-14" @default.
• W2951623434 title "Comments on one-form global symmetries and their gauging in 3d and 4d" @default.
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• W2951623434 doi "https://doi.org/10.21468/scipostphys.6.3.039" @default.
• W2951623434 hasPublicationYear "2019" @default.
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