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Symmetry-Enriched Quantum Spin Liquids in (3+1)d

Hsin, Po-Shen and Turzillo, Alex (2019) Symmetry-Enriched Quantum Spin Liquids in (3+1)d. . (Unpublished)

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We use higher-form global symmetry to classify the symmetry-enriched phases with ordinary global symmetry in bosonic (3+1)d field theory. Different symmetry-enriched phases correspond to different ways to couple the theory to the background gauge field of the ordinary (0-form) symmetry, which include different symmetry-protected topological (SPT) phases. A general (3+1)d theory has one-form and two-form global symmetries A and B, generated by the symmetry surface and line operators. We assume the two-form symmetry is finite. The two-form symmetry implies the theory has the following symmetry defects: (1) surface defects classified by H^2(B,U(1)), they generate a one-form symmetry that acts trivially on all lines. (2) volume defects classified by H^3(B,U(1))′, they generate a 0-form symmetry that neither acts on local operators nor permutes the types of non-local operators. The couplings of a (3+1)d bosonic theory to the background of an ordinary unitary symmetry G can be classified by (η_2,ν_3,ξ)∈H^2_ρ(BG,A)×C^3(BG,B)×H^1_σ(BG,H^3(B,U(1))′) where ρ,σ are fixed G-actions induced by permuting the non-local operators. Δ_σν_3 is subject to a constraint that depends on η_2 and ξ, and ν_3 has an equivalence relation. We determine how the classification and the corresponding 't Hooft anomaly depend on ξ. The set of SPT phases of 0-form symmetry that remain inequivalent depends on the couplings (η_2,ν_3,ξ) of the symmetry-enriched phase and can be obtained from the anomaly of the higher-form symmetries. We illustrate our methods with several examples, including the gapless pure U(1)gauge theory and the gapped Abelian finite group gauge theory. We apply the methods to 't Hooft anomaly matching in (3+1)d non-supersymmetric duality.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Turzillo, Alex0000-0003-4293-4293
Additional Information:We thank Zhen Bi, Xie Chen, Clay Córdova, Anton Kapustin, Kantaro Ohmori, Shu-Heng Shao, Ryan Thorngren and Juven Wang for discussions. The work was supported by 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 P.-S.H. was performed in part at Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20190624-081116757
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:96651
Deposited By: Tony Diaz
Deposited On:24 Jun 2019 17:10
Last Modified:24 Jun 2019 17:10

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