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Comments on one-form global symmetries and their gauging in 3d and 4d

Hsin, Po-Shen and Lam, Ho Tat and Seiberg, Nathan (2019) Comments on one-form global symmetries and their gauging in 3d and 4d. SciPost Physics, 6 (3). Art. No. 039. ISSN 2542-4653. doi:10.21468/SciPostPhys.6.3.039.

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We study 3d and 4d systems with a one-form global symmetry, explore their consequences, and analyze their gauging. For simplicity, we focus on Z_N one-form symmetries. A 3d topological quantum field theory (TQFT) 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 T=T′⊗A^(N,p). Here T′ is a decoupled TQFT, whose lines are neutral under the global symmetry and A^(N,p) is a minimal TQFT with the Z_N one-form symmetry of label p. The parameter p labels the obstruction to gauging the 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 θ-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 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.

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Seiberg, Nathan0000-0003-3897-046X
Additional Information:© 2019 P.-S. Hsin et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation. Received 21-01-2019; Accepted 20-03-2019; Published 29-03-2019. We thank Maissam Barkeshli, Meng Cheng, Clay Córdova, Dan Freed, Davide Gaiotto, Jaume Gomis, Zohar Komargodski, Kantaro Ohmori, Shu-Heng Shao, Zhenghan Wang, and Edward Witten for useful discussions. The work of P.-S.H. was supported by the Department of Physics at Princeton University, the Institute for Advanced Study, and the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, and by the Simons Foundation through the Simons Investigator Award. The work of H.T.L. is supported by a Croucher Scholarship for Doctoral Study, a Centennial Fellowship from Princeton University and the Institute for Advanced Study. The work of N.S. is supported in part by DOE grant DE-SC0009988.
Group:Walter Burke Institute for Theoretical Physics
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Princeton UniversityUNSPECIFIED
Institute for Advanced StudyUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0009988
Issue or Number:3
Record Number:CaltechAUTHORS:20190521-140013223
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95647
Deposited By: Tony Diaz
Deposited On:21 May 2019 21:11
Last Modified:16 Nov 2021 17:14

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