# Derived algebraic geometry of 2d lattice Yang-Mills theory

September 10, 2024

A derived algebraic geometric study of classical $\mathrm{GL}_n$-Yang-Mills
theory on the $2$-dimensional square lattice $\mathbb{Z}^2$ is presented. The
derived critical locus of the Wilson action is described and its local data
supported in rectangular subsets $V =[a,b]\times [c,d]\subseteq \mathbb{Z}^2$
with both sides of length $\geq 2$ is extracted. A locally constant
dg-category-valued prefactorization algebra on $\mathbb{Z}^2$ is constructed
from the dg-categories of perfect complexes on the derived stacks of local
data.

Keywords:

Derived algebraic geometry, derived critical locus, lattice gauge theory, dg-categories, prefactorization algebras