Study of gapped phases of 4d gauge theories using temporal gauging of the ℤN 1-form symmetry

Journal Article · 02 August 2023 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep08(2023)013 · OSTI ID:2418982

Nguyen, Mendel ^[1]; Tanizaki, Yuya  ^[2]; Ünsal, Mithat ^[3]

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1. North Carolina State University, Raleigh, NC (United States); North Carolina State University, Raleigh, NC (United States)
2. Kyoto Univ. (Japan). Yukawa Institute for Theoretical Physics
3. North Carolina State University, Raleigh, NC (United States)

To study gapped phases of 4d gauge theories, we introduce the temporal gauging of Z_N 1-form symmetry in 4d quantum field theories (QFTs), thereby defining effective 3d QFTs with $$\tilde{Z}_N$$ × Z_N 1-form symmetry. In this way, spatial fundamental Wilson and ’t Hooft loops are simultaneously genuine line operators. Assuming a mass gap and Lorentz invariant vacuum of the 4d QFT, the $$\tilde{Z}_N$$ × Z_N symmetry must be spontaneously broken to an order-N subgroup H, and we can classify the 4d gapped phases by specifying H. This establishes the 1-to-1 correspondence between the two classification schemes for gapped phases of 4d gauge theories: one is the conventional Wilson-’t Hooft classification, and the other is the modern classification using the spontaneous breaking of 4d 1-form symmetry enriched with symmetry-protected topological states.

• Research Organization: North Carolina State University, Raleigh, NC (United States)
• Sponsoring Organization: JSPS KAKENHI; USDOE Office of Science (SC), Nuclear Physics (NP)
• Grant/Contract Number: FG02-03ER41260
• OSTI ID: 2418982
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 8 Vol. 2023; ISSN 1029-8479
• Publisher: Springer NatureCopyright Statement
• Country of Publication: United States
• Language: English