Dual equivalence in models with higher-order derivatives

We introduce a class of higher-order derivative models in (2, 1) spacetime dimensions. The models are described by a vector field, and contain a Proca-like mass term which prevents gauge invariance. We use the gauge embedding procedure to generate another class of higher-order derivative models, gauge-invariant and dual to the former class. We show that the results are valid in arbitrary (d, 1) spacetime dimensions when one discards the Chern–Simons and Chern–Simons-like terms. We also investigate duality at the quantum level, and we show that it is preserved in the quantum scenario. Other results include investigations concerning the gauge embedding approach when the vector field couples with fermionic matter, and when one adds nonlinearity.