On the Doubling Phenomenon in Lattice Chern-Simons Theories

TL;DR

This paper investigates the lattice formulation of pure Chern-Simons theory, revealing a doubling phenomenon similar to fermionic theories, and proposes a Maxwell term to eliminate redundant degrees of freedom.

Contribution

It demonstrates the doubling problem in lattice Chern-Simons theories and introduces a Maxwell term as a solution, paralleling Wilson's fermion approach.

Findings

Doubling of bosonic degrees of freedom identified

Adding a Maxwell term removes the doubling

No integrable kernel due to symmetry constraints

Abstract

We analyse the pure Chern-Simons theory on an Euclidean infinite lattice. We point out that, as a consequence of its symmetries, the Chern-Simons theory does not have an integrable kernel. Due to the linearity of the action in the derivatives, the situation is very similar to the one arising in the lattice formulation of fermionic theories. Doubling of bosonic degrees of freedom is removed by adding a Maxwell term with a mechanism similar to the one proposed by Wilson for fermionic models.