IAS CMP/QFT Group Meeting

Abstract: Category theory has long been a standard language for TQFTs with discrete valued degrees of freedom (and more recently, for discrete generalized symmetries). Is the categorical perspective also useful for more ordinary problems in physics, in which the realistic QFTs deal with continuous valued degrees of freedom and non-universal dynamics? Are there such traditional problems that actually require categories to be resolved? In this talk I will begin by phrasing the traditional lattice QFTs in categorical terms; then I will introduce Villainization and spinon-decomposition from the perspective of higher anafunctors and generalized relative cohomologies. While these are just reformulations of known models, next I will show how such a categorical framework will naturally provide us solutions to long standing problems in the lattice QCD community: Lattice definitions of baryons in pion NLsM and instantons in SU(N) Yang-Mills---we are working towards implementing these categorically refined models in actual numerics, with the aid of numerical renormalization facilitated by machine learning. I will also show how the relative cohomology behind the lattice Yang-Mills reduces to the usual group cohomology of the Dijkgraaf-Witten model when the gauge group becomes finite.