Princeton University High Energy Theory Seminar

Abstract: I will introduce a new framework to understand what a lattice QFT “really is” in relation to continuum QFT, by elevating the physically intuitive idea behind the Villain model into the mathematical language of higher category theory. Long standing problems in the lattice community on unambiguously defining topological operators on the lattice---most notably instanton density in lattice QCD---are solved by refining the traditional models using this categorical language, in a natural and necessary manner. (Yes, this means category theory is "crucially useful" to traditional problems in physics.)

The next stage is to implement such refined models into actual numerics. Real space numerical renormalization, aided with some simple machine learning, fits naturally into our categorical framework, and provides a nice solution to some challenging technicalities in the implementation. I will show our preliminary numerical results on the refined CP^N model, as a prototypical study for the refined Yang-Mills theory.

Reference: 2406.06673 and on-going works