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Medientyp:
E-Artikel
Titel:
Comments on one-form global symmetries and their gauging in 3d and 4d
Beteiligte:
Hsin, Po-Shen;
Lam, Ho Tat;
Seiberg, Nathan
Erschienen:
Stichting SciPost, 2019
Erschienen in:
SciPost Physics, 6 (2019) 3
Sprache:
Nicht zu entscheiden
DOI:
10.21468/scipostphys.6.3.039
ISSN:
2542-4653
Entstehung:
Anmerkungen:
Beschreibung:
We study 3d and 4d systems with a one-form global symmetry, exploretheir consequences, and analyze their gauging. For simplicity, we focuson \mathbb{Z}_NℤNone-form symmetries. A 3d topological quantum field theory (TQFT)\mathcal{T}𝒯with such a symmetry has NNspecial lines that generate it. The braiding of these lines and theirspins are characterized by a single integerppmodulo 2N2N.Surprisingly, if \gcd(N,p)=1gcd(N,p)=1the TQFT factorizes \mathcal{T}=\mathcal{T}'\otimes \mathcal{A}^{N,p}𝒯=𝒯′⊗𝒜N,p.Here \mathcal{T}'𝒯′is a decoupled TQFT, whose lines are neutral under the global symmetryand \mathcal{A}^{N,p}𝒜N,pis a minimal TQFT with the \mathbb{Z}_NℤNone-form symmetry of label pp.The parameter pplabels the obstruction to gauging the \mathbb{Z}_NℤNone-form symmetry; i.e. it characterizes the ’t Hooft anomaly of theglobal symmetry. When p=0p=0mod 2N2N,the symmetry can be gauged. Otherwise, it cannot be gauged unless wecouple the system to a 4d bulk with gauge fields extended to the bulk.This understanding allows us to consider SU(N)SU(N)and PSU(N)PSU(N)4d gauge theories. Their dynamics is gapped and it is associated withconfinement and oblique confinement – probe quarks are confined. In thePSU(N)PSU(N)theory the low-energy theory can include a discrete gauge theory. Wewill study the behavior of the theory with a space-dependent\thetaθ-parameter,which leads to interfaces. Typically, the theory on the interface is notconfining. Furthermore, the liberated probe quarks are anyons on theinterface. The PSU(N)PSU(N)theory is obtained by gauging the \mathbb{Z}_NℤNone-form symmetry of the SU(N)SU(N)theory. Our understanding of the symmetries in 3d TQFTs allows us todescribe the interface in the PSU(N)PSU(N)theory.