Ultraviolet properties of N=8 supergravity at five loops

By Z. Bern, J. J. Carrasco, Wei-ming Chen, Alex Edison, H. Johansson, Julio Parra-Martinez, R. Roiban, M. Zeng. Physical Review D, 2018

149 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/79de446d7761a81682c2c500403e65f64ee67d78

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. A. Luna
2. R. Roiban
3. C. Cheung
4. M. Zeng
5. A. Eichhorn
6. Chia-Hsien Shen
7. Z. Bern
8. L. Canet

In Nuclear and High Energy Physics

1. C. Cheung
2. A. Eichhorn
3. R. Roiban
4. A. Luna
5. Chia-Hsien Shen
6. W. Metzner
7. M. Tissier
8. N. Dupuis

Citations in the corpus

• Spinning black hole binary dynamics, scattering amplitudes, and effective field theory (2020, background): “of much simpler gauge-theory ones, enabling explicit (super)gravity calculations at remarkably high orders of perturbation theory [44, 45].”
• The nonperturbative functional renormalization group and its applications (2020, background): “, N = 8 supergravity, is also being explored as a way to reduce the number of ultraviolet divergences, see [1081] and references therein.”
• Black hole binary dynamics from the double copy and effective theory (2019, methodology): “We expect that our approach to integrand construction via double copy and unitarity should scale well to quite high loop orders, as highlighted by their application to supergravity theories up to five-loop order [40].”