Ultraviolet properties of N=8 supergravity at five loops

Abstract

We use the recently developed generalized double-copy construction to obtain an improved representation of the five-loop four-point integrand of N = 8 supergravity whose leading ultraviolet behavior we analyze using state-of-the-art loop-integral expansion and reduction methods. We find that the five-loop critical dimension where ultraviolet divergences first occur is D c = 24/5, corresponding to a D 8 R 4 counterterm. This ultraviolet behavior stands in contrast to the cases of four-dimensional N = 4 supergravity at three loops and N = 5 supergravity at four loops whose improved ultraviolet behavior demonstrates enhanced cancellations beyond implications from standard-symmetry considerations. We express this D c = 24/5 divergence in terms of two relatively simple positive-definite integrals reminiscent of vacuum integrals, excluding any additional ultraviolet cancellations at this loop-order. We note nontrivial relations between the integrals describing this leading ultraviolet behavior and integrals describing lower-loop behavior. This observation suggests not only a path towards greatly simplifying future calculations at higher loops, but may even allow us to directly investigate ultraviolet behavior in terms of simplified integrals, avoiding the construction of complete integrands.

Monopoles, shockwaves and the classical double copy

“…Like the solutions of eq. (15,17), this contains an inverse power of the coupling, and also has a pure power-like dependence in the spherical radius r, where the power itself can be dictated on dimensional grounds 8 . Given the lack of any precedent for how to formulate a non-perturbative double copy, ref.…”

“…[48] left as merely speculative the suggestion that the biadjoint monopoles of eqs. (15,17) are related to the Wu-Yang monopole. Our aim here is to examine this systematically, and the starting point will be the above-mentioned fact that shockwave solutions are known to double copy.…”

Double copy of massive scalar QCD

“…This applies to any amplitude that involves an odd number of B-fields, so we will only write down the non-vanishing ones. Similarly, the 4-point amplitude of two massive scalars and two gluon (7) gives the following gravitational amplitudes after the double copy,…”

“…This procedure hinges upon finding a representation of the gauge theory amplitudes built from trivalent graphs with color and kinematic numerator factors fulfilling Jacobi-like identities. It was originally observed for pure gauge theories (with and without supersymmetry) which double copied to pure (super)-gravities and has proven to be an efficient tool also beyond tree-level (where proofs of the double-copy exist [4,5]) to generate amplitude integrands at high-loop orders in the maximal supersymmetric case [6,7]. By now the doublecopy has been observed in a large set of gravitational theories involving massless fields, including pure gravity [8], pure and matter coupled supergravities [8][9][10] as well as Einstein-Yang-Mills theories [11][12][13][14].…”

String correlators: recursive expansion, integration-by-parts and scattering equations

“…The fusion W 1 , W 2 merges two color traces into a single trace since it is a linear combination of PT(ρ) with ρ ∈ perm(W 1 ∪ W 2 ). As a concrete example, we consider the fusion of PT (12) and PT(345): } Figure 1: Gluing two cycles W 1 and W 2 into a single one. A directed edge from node i to j represents a factor of 1 z ij while a wavy edge is defined by Eq.…”