Time: 2:00-3:30 pm, September 11/12/13, 2023

A long standing problem in lattice QCD is there is no    natural lattice definition of the instanton operator. This problem    hampers our understanding of QCD confinement. I will show how this    long standing problem is -- and has to be -- solved by higher    category theory. In this language, the solution is a deep    generalization of the Villain model familiar in condensed matter    physics. Using the same structure, one can also define the    Chern-Simons term in lattice Yang-Mills, as well as the skyrmion    operator and the Wess-Zumino-Witten term in lattice SU(N) non-linear    sigma model.

In a larger scope, I will sketch a systematic program    to renew our understanding of the relation between continuum QFT and    lattice QFT. I will explain how this understanding has the hope to    lead to substantial progress in the field of constructive QFT, which    aims at defining QFT in the continuum, such as 4D Yang-Mills.