Derived algebraic geometry of 2d lattice Yang-Mills theory
Abstract
Abstract A derived algebraic geometric study of classical $$\textrm{GL}_n$$ GL n -Yang-Mills theory on the 2-dimensional square lattice $${\mathbb {Z}}^2$$ Z 2 is presented. The derived critical locus of the Wilson action is described and its local data supported in rectangular subsets $$V =[a,b]\times [c,d]\subseteq {\mathbb {Z}}^2$$ V = [ a , b ] × [ c , d ] ⊆ Z 2 with both sides of length $$\ge 2$$ ≥ 2 is extracted. A locally constant dg-category-valued prefactorization algebra on $${\mathbb {Z}}^2$$ Z 2 is constructed from the dg-categories of quasi-coherent complexes on the derived stacks of local data.
Fields of Study & Subjects
Advanced Algebra and Geometry
Advanced Topics in Algebra
Black Holes and Theoretical Physics
Publication details
- Journal / source
- Selecta Mathematica
- Volume
- 32
- Issue
- 3
- Publication date
- 29 June 2026
- Language
- EN