Collinear and soft divergences in perturbative quantum gravity

Abstract

Collinear and soft divergences in perturbative quantum gravity are investigated to arbitrary orders in amplitudes for wide-angle scattering, using methods developed for gauge theories. We show that collinear singularities cancel when all such divergent diagrams are summed over, by using the gravitational Ward identity that decouples unphysical polarizations from the S-matrix. This analysis generalizes a result previously demonstrated in the eikonal approximation. We also confirm that the only virtual graviton corrections that give soft logarithmic divergences are of the ladder and crossed ladder type.

On-shell techniques and universal results in quantum gravity

“…Although quantum gravity is at times an exhaustive discipline [48] is important to realize that the treament using modern on-shell methods presents a huge advantage in efficiency. For example it might be possible to apply some of our techniques to the recent paper [53] and more generally it might be of interest to reconsider many historical computations in the light of new computational methods. The recent progress in computational techniques will here most likely allow an extended analysis.…”

Light-like scattering in quantum gravity

“…Including the dressing of M (2) (q) by permutations of one graviton exchange, it was shown in [55] that there is again an exponentiation of the simple exchange…”

“…Our guide in this approach is the discussion of the next-to-leading eikonal amplitude by Akhoury et al in [55]. 3 This method can be readily generalized to include the quantum terms within the same diagrams as well as the purely quantum diagrams (the bubble diagrams) at the same order.…”

“…The infrared divergences of gravitational theories have been studied in [49][50][51][52][53]. At one-loop the amplitude is the sum, M (2) X = S M (1) +H, consisting of an infrared divergent part from the soft region in (4.10), S = (tµ −2 ) − /(t 2 ) times M (1) (the tree-level one-graviton amplitude is evaluated in appendix A.3) and a finite hard part H. When forming cross-sections, we know how to resolve them.…”

New insights into soft gluons and gravitons

“…Infrared singularities in gravity were first examined in [8], and there has recently been a revival of interest aimed at describing gravitational physics using the same language as is used in nonabelian gauge theories [9,20]. It has now been firmly established that the exponent of the soft function in gravity is one-loop exact i.e.…”