Adjoint QCD${}_4$, Deconfined Critical Phenomena, Symmetry-Enriched Topological Quantum Field Theory, and Higher Symmetry-Extension

Abstract

Recent work explores the candidate phases of the 4d adjoint quantum chromodynamics (QCD${}_4$) 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 QCD${}_4$ under a renormalization-group (RG) flow from high energy. In this work, we generalize the symmetry-extension method [arXiv:1705.06728] to higher symmetries, and formulate 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 $A{\mathcal{P}}_2(B_2)$ nor ${\mathcal{P}}_2(B_2)$ can be fully trivialized, with the background 1-form field $A$, Pontryagin square ${\mathcal{P}}_2$ and 2-form field $B_2$. 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 critical points (dQCP), quantum spin liquids (QSL) or quantum fermionic liquids in condensed matter, and ultraviolet-infrared (UV-IR) duality in 3+1 spacetime dimensions.

23 pages, 12 figures, 5 tables. v4: ~ PRD version, with improvements and a correction in Table IV and V. See companions arXiv:1812.11967, arXiv:1812.11968 and arXiv:1904.00994

References in corpus (10)

• Generalized Global Symmetries
• "Deconfined" quantum critical points
• Emergent (anomalous) higher symmetries from topological orders and from dynamical electromagnetic field in condensed matter systems
• Anomalies of discrete symmetries in various dimensions and group cohomology
• Adjoint QCD${}_4$, Deconfined Critical Phenomena, Symmetry-Enriched Topological Quantum Field Theory, and Higher Symmetry-Extension
• Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
• The infrared regime of SU(2) with one adjoint Dirac flavour
• Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theory
• On 2-form gauge models of topological phases
• Homotopy Theoretic Classification of Symmetry Protected Phases

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