2018/12/31 by Zheyan Wan, Juven Wang · 1 citation
Physics and Astronomy · Mathematics · #hep-th #cond-mat.str-el #hep-lat #hep-ph #math.AT
paper · pdf · doi:10.1103/physrevd.99.065013
published as Phys. Rev. D 99, 065013 (2019) · 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
arxiv created 2019/04/25 · arxiv updated 2019/04/26
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 (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 P2(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 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.