Speaker
Description
I will introduce a systematic way to rethink and refine lattice QFT, in order to make better connection to continuum QFT, by elevating the idea behind the Villain model into the language of higher category theory. Our primary purpose is to find unambiguous definitions for topological operators (and hence the associated symmetries and anomalies) on the lattice---the most notable example is the long existing problem of defining instanton density in lattice QCD. The next step is to implement such refined models into actual numerics. Real space numerical renormalization, aided with some simple machine learning, fits naturally into this categorical framework, and provides a nice solution to some challenging technicalities in the implementation. I will show some preliminary numerical studies on the refined CP^N model, as a prototypical study for the refined Yang-Mills theory; already at this preliminary stage, we obtained a much more detailed understanding and control of the renormalization on lattice, compared to the traditional “scale setting” protocol.