Mimetic discretization of the Abelian Chern-Simons theory and link invariants

TL;DR

This paper develops a mimetic discretization of the Abelian Chern-Simons theory on a lattice, providing explicit formulas for link invariants and exploring metric discretization for knot theory applications.

Contribution

It introduces a lattice formulation of Abelian Chern-Simons theory with a consistent differential forms approach, including explicit link invariant expressions.

Findings

Explicit lattice expressions for Gauss Linking Number

A framework for discretizing metric structures in the space of vector densities

Potential for deriving knot and link invariants in lattice models

Abstract

A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consistent definition of the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which correspond to their continuum counterparts are given. A discussion of the discretization of metric structures in the space of transverse vector densities is presented. The study of these metrics could serve to obtain explicit formulae for knot an link invariants in the lattice.