Witten diagrams in momentum space and one graviton exchange between scalars in Weyl invariant unimodular gravity

TL;DR

This paper computes the s-channel Witten diagram for graviton exchange between scalars in Weyl invariant unimodular gravity, showing it matches the result in General Relativity and providing a compact momentum space expression.

Contribution

It demonstrates that the graviton exchange diagram in Weyl invariant unimodular gravity is equivalent to that in General Relativity and derives a simplified momentum space formula.

Findings

The diagram value matches that in General Relativity.

A compact expression in Mandelstam variables is obtained.

The calculation confirms the equivalence of the two theories in this context.

Abstract

We tackle head-on the computation of the $s$-channel Witten diagram in momentum space corresponding to the exchange of a graviton between minimally coupled scalars in Weyl invariant unimodular gravity. By means of a lengthy calculation, we show first that the value of the diagram in question is the same as in General Relativity and, then, we obtain a compact expression for it in terms of the Mandelstam variables.