Ultraviolet behavior of transverse gravity

TL;DR

This paper investigates the divergence structure of transverse gravity theories, revealing that only Einstein's gravity and WTDiff are finite at one-loop order when the cosmological constant is zero, due to their enhanced symmetries.

Contribution

It identifies the conditions under which transverse gravity theories are one-loop finite, highlighting the special roles of Einstein's gravity and WTDiff with enhanced symmetries.

Findings

Einstein's gravity is on-shell finite at one-loop.

WTDiff theory is also on-shell finite with local Weyl invariance.

Additional scalar degrees of freedom are absent in these finite theories.

Abstract

The structure of the divergences for transverse theories of gravity is studied to one-loop order. These theories are invariant only under those diffeomorphisms that enjoy unit Jacobian determinant (TDiff), so that the determinant of the metric transforms as a true scalar instead of a density. Generically, the models include an additional scalar degree of freedom contained in the metric besides the usual spin two component. When the cosmological constant is fine tuned to zero, there are only two theories which are on shell finite, namely the one in which the symmetry is enhanced to the full group of diffeomorphisms, i.e. Einstein's gravity, and another one denoted by WTDiff which enjoys local Weyl invariance. Both of them are free from the additional scalar.