Anyonic-String/Brane Träumerei: Quantum 4d Yang-Mills Gauge Theories and Time-Reversal Symmetric 5d TQFT

My talk will aim to be a friendly introduction for condensed matter friends, mathematicians, and QFT theorists alike --- I shall quickly review and warm up the use of higher symmetries and anomalies of gauge theories and condensed matter systems. Then I will present the results of recent work [arXiv:1904.00994].

We explore 4d time-reversal symmetric pure Yang-Mills (YM) gauge theories of an SU(2) gauge group with a second-Chern-class topological term at $\theta=\pi (SU(2) \theta=\pi YM)$ living as boundary conditions of 5d topological state (5d bordism invariants of mod 2 class, or 5d higher-1-form-center-symmetry-protected interacting (SPT) "topological superconductor" in condensed matter). We find their "Fantastic Four Siblings" with four sets of new higher "anomalies" associated with the Kramers singlet/doublet and bosonic/fermionic properties of Wilson lines. Via Weyl's gauge principle, by dynamically gauging the 1-form center symmetry, we transform a 5d bulk SPTs into a symmetry-enriched topologically ordered state (SETs) as 5d higher-gauge TQFT. Apply the tool introduced in [arXiv:1612.09298], we derive new exotic anyonic statistics of extended objects such as 2-worldsheet of strings and 3-worldvolume of branes, which physically characterize the 5d SETs. We discover new triple and quadruple link invariants potentially associated with the underlying 5d TQFTs, hinting an intrinsic relation between non-supersymmetric 4d pure YM and topological links in 5d. We provide lattice simplicial complex and "condensed matter" regularizations and then comment on 4d gauge dynamics.

Affiliation

Member, School of Natural Sciences, IAS

Juven Wang