Transverse(Diff) theories of gravity

Abstract

Let us summarize and collect our results into a unified picture. In the first place, since TDiff theories have a quantum inspiration. it is natural to investigate their quantum behavior. As mentioned in the introduction, the good properties of the TDiff group to describe a (quantum) unitary theory of gravitation were already established, in particular the infrared-finiteness. However, one still has to adress the issue of the ultraviolet behavior. We calculated this behavior at the 1-loop level and found it to be worse than General Relativity, safe for the very specific case of WTDiff. Indeed, General Relativity iis still 1-loop on-shell finite in the absence of matter (it is divergent at 2-loops, or in the presence of matter), while here the appearance of an addtional scalar mode generates divergences. On the way, we reproduced rather involved calculations by other authors using background field and heat-kernel techniques, like (74), (22) and (10). We noted that with an adequate use of modern algebraic computer packages, such as xTensor (57), these become almost straightforward.