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

摘要

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 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 A P 2 ( B 2 ) nor P 2 ( B 2 ) can be fully trivialized, with the background 1-form field A , Pontryagin square 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 criticality and ultraviolet-infrared duality in 3 + 1 spacetime dimensions.