Dual equivalence in models with higher-order derivatives

TL;DR

This paper introduces higher-order derivative models in (2,1) dimensions, demonstrating gauge invariance, duality, and quantum consistency, with extensions to matter coupling and nonlinearity.

Contribution

It develops a gauge embedding method to generate gauge-invariant dual models from non-invariant higher-order derivatives, extending to arbitrary (d,1) dimensions without Chern-Simons terms.

Findings

Dual models are gauge-invariant and dual to original models.

Duality is preserved at the quantum level.

Gauge embedding works with matter coupling and nonlinearity.

Abstract

We introduce a class of higher-order derivative models in (2,1) space-time 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) space-time 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.