Quadratic gravity and restricted Weyl symmetry

Abstract

In this paper, we investigate the relationship between quadratic gravity and a restricted Weyl symmetry where a gauge parameter [Formula: see text] of Weyl transformation satisfies a constraint [Formula: see text] in a curved spacetime. First, we briefly review a model with a restricted gauge symmetry on the basis of QED, where a [Formula: see text] gauge parameter [Formula: see text] obeys a similar constraint [Formula: see text] in a flat Minkowski spacetime, and explain that the restricted gauge symmetry removes one on-shell mode of gauge field, which together with the Feynman gauge leaves only two transverse polarizations as physical states. Next, it is shown that the restricted Weyl symmetry also eliminates one component of a dipole field in quadratic gravity around a flat Minkowski background, leaving only a single scalar state. Finally, we show that the restricted Weyl symmetry cannot remove any dynamical degrees of freedom in static background metrics by using the zero-energy theorem of quadratic gravity. This fact also holds for the Euclidean background metrics without imposing the static condition.