Degenerate higher-order Maxwell-Einstein theories

TL;DR

This paper classifies and constructs degenerate higher-order Maxwell-Einstein theories, extending scalar-tensor theories to gauge fields, identifying conformally invariant models, and exploring transformations that generate ghost-free theories.

Contribution

It provides a comprehensive classification of degenerate Maxwell-Einstein theories with higher derivatives, including conformally invariant and transformation-generated models.

Findings

Classified all degenerate higher-order Maxwell-Einstein Lagrangians.

Identified all conformally invariant degenerate interactions.

Generated new ghost-free theories via disformal transformations.

Abstract

We classify higher-order Maxwell-Einstein theories linear in the curvature tensor and quadratic in the derivatives of the electromagnetic field strength whose kinetic matrices are degenerate. This provides a generalisation of quadratic degenerate higher-order scalar-tensor theories for a U(1) gauge field. After establishing a classification of the independent Lagrangians, we obtain all the theories with at most third order field equations involving only second order derivatives of the metric, thus generalising Horndeski's quadratic theory for a gauge field. Some of these are shown to be conformally invariant. We then classify degenerate non-minimally coupled interactions, obtaining all conformally invariant ones. Finally, we investigate the effect of U(1)-preserving disformal transformations on these degenerate Lagrangians. The ``mimetic" singular transformations are obtained and new ghost-free degenerate theories are generated.