Description
Instanton Operator in Lattice QCD from Higher Anafunctor -- or, How to Put Continuum QFT onto Lattice
Abstract:
A long standing problem in lattice QCD is there is no natural lattice definition of instanton operator. This problem hampers our understanding of, e.g., QCD confinement. I will show how this traditional problem is -- and has to be -- solved by higher category theory, in particular by the use of higher anafunctors. Related to this, one can also define the Chern-Simons term in Yang-Mills theory, as well as the skyrmion operator and Wess-Zumino-Witten term in SU(N) non-linear sigma model.
More broadly, using the language higher anafunctors, I will sketch a systematic program to put continuum QFT (note, not just TQFT in the IR, but QFT with general dynamics) onto the lattice, especially for non-linear sigma models and gauge theories with continuous-valued fields, while retaining all the topological operators. I will discuss two important future prospects: The first is how one might unify this general picture and the usual use of categories in the TQFT context with discrete degrees of freedom and/or symmetries. The second is why this picture has the hope to lead to non-trivial progress in the field of constructive QFT, which aims at defining QFT in the continuum, such as 4D Yang-Mills.
