Two-loop renormalization of quantum gravity simplified

Abstract

The coefficient of the dimensionally regularized two-loop R 3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when non-dynamical three forms are added to the theory, or when a pseudo-scalar is replaced by the anti-symmetric two-form field to which it is dual. This phenomenon involves evanescent operators, whose matrix elements vanish in four dimensions, including the Gauss-Bonnet operator which is also connected to the trace anomaly. On the other hand, these effects appear to have no physical consequences in renormalized scattering processes. In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is simple. In this paper, we explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators.

Manifesting enhanced cancellations in supergravity: integrands versus integrals

“…Despite this we do not know the answer to the basic question of at which loop order various gravity theories actually diverge. In addition, when divergences occur in graviton amplitudes we now know that they have unusual properties, including dependence on evanescent effects [2,3] and suspected links to anomalies [4][5][6][7]. Even more interesting are indications in certain supergravity theories that the loop order where the first divergence occurs is higher than previous expectations [8][9][10].…”

“…However, this is of secondary concern because usually we are interested in studying the very first potential divergence of a supergravity theory. (There are some subtleties with evanescent effects feeding into divergences which require some care [2,3].) The most interesting cases, such as N = 8 supergravity at five loops in D = 24/5, automatically have no subdivergences because of a lack of lower-loop divergences.…”

Graviton bending in quantum gravity from one-loop amplitudes

“…where again b is the gauge-invariant impact parameter and c 1 , c 2 , c 3 are, respectively, the coefficients of the scalar massless bubble integral I 2 (s), the scalar massless triangle integral I 3 (s) and the scalar massive triangle integral I 3 (s, M ) in Eq. (6).…”

“…c1, c2, c3 are, respectively, the coefficients of the scalar massless bubble integral I2(s), the scalar massless triangle integral I3(s) and the scalar massive triangle integral I3(s, M ) in Eq. (6). In each case, the first column denotes the projectiles, while the second column denotes the particles crossing the cut.…”

Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO

“…In particular the efficient double copy construction based on the Bern-Carrasco-Johansson (BCJ) color-kinematical duality [26][27][28] yields the integrands of gravitational scattering amplitudes from the simpler quantities in Yang-Mills theories, allowing for high order results in (super)gravity (see e.g. the recent [29,30]). In view of these innovations it is natural to ask to what extent these modern scattering amplitude techniques may be put to work to the classical scattering problem in general relativity and in turn to the perturbative construction of effective potentials discussed above.…”