Seminar, Juven Wang (Harvard University), Quantum 4d Yang-Mills Theories and Time-Reversal Symmetric 5d Higher-Gauge TQFT


Tuesday, October 22, 2019, 3:30pm


Jefferson 356

Juven Wang

Title: Quantum 4d Yang-Mills Theories and Time-Reversal Symmetric 5d Higher-Gauge TQFT

Abstract: We explore 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-reversal symmetric pure YM of an SU(2) gauge group with a second-Chern-class topological term at θ=π (SU(2)θ=π YM), by turning on background fields for both the time-reversal (i.e., on unorientable manifolds) and 1-form center global symmetry. We comment on that such 4d Yang-Mills dynamics cannot be trivially confined gapped. The work is based mainly on, also and  

In more details: We find Four Siblings of SU(2)θ=π YM with distinct couplings to background fields, labeled by (K1,K2): K1=0,1 specifies Kramers singlet/doublet Wilson line and new mixed higher 't Hooft anomalies; K2=0,1 specifies boson/fermionic Wilson line and a new Wess-Zumino-Witten-like counterterm. Higher anomalies indicate that to realize all higher n-global symmetries locally on n-simplices, the 4d theory becomes a boundary of a 5d higher-symmetry-protected topological state (SPTs, as an invertible topological quantum field theory or a cobordism invariant in math, or as a 5d higher-symmetric interacting topological superconductor in condensed matter). Via Weyl's gauge principle, by dynamically gauging the 1-form symmetry, we transform a 5d bulk SRE SPTs into an LRE symmetry-enriched topologically ordered state (SETs); thus we obtain the 4d SO(3)θ=π YM-5d LRE-higher-SETs coupled system with higher-form gauge fields. We further derive new exotic anyonic statistics of extended objects such as 2-worldsheet of strings and 3-worldvolume of branes, physically characterizing the 5d SETs. We discover triple and quadruple link invariants potentially associated with the underlying 5d higher-gauge TQFTs, hinting a new intrinsic relation between non-supersymmetric 4d pure YM and topological links in 5d. We provide 4d-5d lattice simplicial complex regularizations and bridge to 4d SU(2) and SO(3)-gauged quantum spin liquids as 3+1 dimensional realizations.

Related to my IAS seminar: 



Flyer_20191022.pdf142 KB