Intersections forms and the geometry of lattice Chern-Simons theory

TL;DR

This paper demonstrates how Abelian Chern-Simons theory can be formulated on a lattice as a topological field theory, preserving key properties and solvability of the continuum version.

Contribution

It introduces a lattice formulation of Abelian Chern-Simons theory that maintains gauge invariance and topological features, providing an exactly solvable model.

Findings

Lattice Abelian Chern-Simons theory is topologically equivalent to the continuum.

The lattice theory is exactly solvable with the same degrees of freedom as the continuum.

Gauge invariance is preserved in the lattice formulation.

Abstract

We show that it is possible to formulate Abelian Chern-Simons theory on a lattice as a topological field theory. We discuss the relationship between gauge invariance of the Chern-Simons lattice action and the topological interpretation of the canonical structure. We show that these theories are exactly solvable and have the same degrees of freedom as the analogous continuum theories.