• Open Access

Adjoint QCD4, deconfined critical phenomena, symmetry-enriched topological quantum field theory, and higher symmetry extension

Zheyan Wan and Juven Wang
Phys. Rev. D 99, 065013 – Published 25 March 2019

Abstract

Recent work explores the candidate phases of the 4D adjoint quantum chromodynamics (QCD4) with an SU(2) gauge group and two massless adjoint Weyl fermions. Both Cordova-Dumitrescu and Bi-Senthil propose possible low energy 4D topological quantum field theories (TQFTs) to saturate the higher ’t Hooft anomalies of adjoint QCD4 under a renormalization-group flow from high energy. In this work, we generalize the symmetry-extension method of Wang-Wen-Witten [Phys. Rev. X 8, 031048 (2018)] to higher symmetries, and formulate a higher group cohomology and cobordism theory approach to construct higher-symmetric TQFTs. We prove that the symmetry-extension method saturates certain anomalies, but also prove that neither AP2(B2) nor P2(B2) can be fully trivialized, with the background 1-form field A, Pontryagin square P2, and 2-form field B2. Surprisingly, this indicates an obstruction to constructing a fully 1-form center and 0-form chiral symmetry (full discrete axial symmetry) preserving 4D TQFT with confinement, a no-go scenario via symmetry extension for specific higher anomalies. We comment on the implications and constraints on deconfined quantum criticality and ultraviolet-infrared duality in 3+1 spacetime dimensions.

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  • Received 23 January 2019
  • Corrected 20 July 2020

DOI:https://doi.org/10.1103/PhysRevD.99.065013

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Interdisciplinary PhysicsParticles & FieldsCondensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Corrections

20 July 2020

Correction: The end of the heading for Appendix A was inadvertently deleted during the production cycle and has been restored.

Authors & Affiliations

Zheyan Wan1 and Juven Wang2,*

  • 1School of Mathematical Sciences, USTC, Hefei 230026, China
  • 2School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA and Center of Mathematical Sciences and Applications, Harvard University, Massachusetts 02138, USA

  • *juven@ias.edu

See Also

Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions

Juven Wang, Xiao-Gang Wen, and Edward Witten
Phys. Rev. X 8, 031048 (2018)

Article Text

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Issue

Vol. 99, Iss. 6 — 15 March 2019

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