Chern-Simons term and Topological Charge on the Lattice

TL;DR

This paper explores the relationship between Seiberg's and L"uschers' definitions of topological charge on the lattice, highlighting their connection and implications for Chern-Simons number in baryon number violation.

Contribution

It clarifies the relationship between two lattice topological charge definitions and extends their application to include Chern-Simons number relevant for baryon number violation.

Findings

Seiberg's and L"uschers' charge definitions are related up to the section of the bundle.

The work extends the lattice topological charge concept to include Chern-Simons number.

Provides insights useful for studying baryon number violating processes.

Abstract

In a somewhat overlooked work by Seiberg, a definition of the topological charge for SU(N) lattice fields was given. Here, it is shown that Seibergs and L\"{u}schers charge definition are related up to the section of the bundle. With the continued interest in baryon number violating processes, Seibergs paper is useful since it allows for a Chern-Simons number also.