Higher Derivative Chern--Simons Extensions

TL;DR

This paper investigates higher-derivative extensions of the 3D Abelian Chern--Simons invariant, revealing a unique third-derivative term and analyzing a combined model with Maxwell theory that exhibits both massless and ghost excitations.

Contribution

It introduces and analyzes the unique third-derivative extension of the Chern--Simons invariant and explores its implications when combined with Maxwell theory, including excitation spectra.

Findings

The third-derivative extension I_ECS is unique and depends only on the field strength.

The combined model with Maxwell theory has a massless mode and a massive ghost.

The Hamiltonian analysis confirms the excitation spectrum and provides the stress tensor.

Abstract

We study the higher-derivative extensions of the D=3 Abelian Chern--Simons topological invariant that would appear in a perturbative effective action's momentum expansion. The leading, third-derivative, extension I_ECS turns out to be unique. It remains parity-odd but depends only on the field strength, hence no longer carries large gauge information, nor is it topological because metric dependence accompanies the additional covariant derivatives, whose positions are seen to be fixed by gauge invariance. Viewed as an independent action, I_ECS requires the field strength to obey the wave equation. The more interesting model, adjoining I_ECS to the Maxwell action, describes a pair of excitations. One is massless, the other a massive ghost, as we exhibit both via the propagator and by performing the Hamiltonian decomposition. We also present this model's total stress tensor and energy. Other actions involving I_ECS are also noted.