Topic: lattice Yang–Mills theory

Singular configuration spaces require extensions of the usual operators and dynamics of quantum mechanics. Using metric-measure calculus, this work constructs states, observables and unitary evolution under suitable assumptions. A curvature-based technique bounds spectral gaps after symmetry reduction. Examples include a constrained oscillator, lattice Yang–Mills theory and fractional-dimensional spaces; the talk also considers prospective connections with the Yang–Mills mass-gap problem and gravity.

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 a