Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N = 8 Supergravity
By Z. Bern, J. J. Carrasco, L. Dixon, H. Johansson, R. Roiban. 2008
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Using the method of maximal cuts, we obtain a form of the three-loop four-point scattering amplitude of $\mathcal{N}=8$ supergravity in which all ultraviolet cancellations are made manifest. The Feynman loop integrals that appear have a graphical representation with only cubic vertices, and numerator factors that are quadratic in the loop momenta, rather than quartic as in the previous form. This quadratic behavior reflects cancellations beyond those required for finiteness, and matches the quadratic behavior of the three-loop four-point scattering amplitude in $\mathcal{N}=4$ super-Yang-Mills theory. By direct integration we confirm that no additional cancellations remain in the $\mathcal{N}=8$ supergravity amplitude, thus demonstrating that the critical dimension in which the first ultraviolet divergence occurs at three loops is ${D}_{c}=6$. We also give the values of the three-loop divergences in $D=7$, 9, 11. In addition, we present the explicitly color-dressed three-loop four-point amplitude of $\mathcal{N}=4$ super-Yang-Mills theory.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/e6381d980677c9ad8646ddf62f7bdff431979a4d
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Citations in the corpus
- Automorphic properties of low energy string amplitudes in various dimensions (2010, background): “This has to be consistent with the residue of the ǫ pole in the three-loop supergravity calculation in [36], which is proportional to ζ(3).”
- Introduction to Soft-Collinear Effective Theory (2014, background): “It is interesting to observe that the full three-loop four-jet amplitudes in N = 4 super Yang-Mills theory were already reduced to linear combinations of a small number of scalar integrals [110].”
- Factorization properties of soft graviton amplitudes (2011, background): “A possible application of these ideas is, for example, that of settling the question of whether N = 8 supergravity is ultraviolet finite [8, 9, 10, 11, 12].”
- Erratum: On the structure of infrared singularities of gauge-theory amplitudes (2009, background): “4 below) might hold to all orders was mentioned in passing in the introduction of [12], without presenting any supporting arguments.”