Higher derivative Chern–Simons extensions

We study the higher-derivative extensions of the D=3 Abelian Chern–Simons topological invariant that would appear in a perturbative effective actionʹs momentum expansion. The leading, third-derivative, extension IECS 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, IECS requires the field strength to obey the wave equation. The more interesting model, adjoining IECS 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 modelʹs total stress tensor and energy. Other actions involving IECS are noted, as is the corresponding extension of the D=4 θ-term.