Instanton and Chern-Simons in Lattice Yang-Mills Theory from Higher Category Theory

Jing-Yuan Chen develops a systematic relationship between continuum and lattice quantum field theories using higher categories and higher anafunctors. The construction records the different ways a lattice field can interpolate into the continuum, allowing continuum topological operators to be defined naturally on a lattice. It resolves the definition of instanton and Chern–Simons terms in lattice Yang–Mills theory using a variant of multiplicative bundle gerbes. With discrete fields it recovers Dijkgraaf–Witten and Turaev–Viro theories, suggesting a common categorical treatment of continuous and discrete degrees of freedom.