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Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity

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arxiv 0808.4112 v1 pith:JFYSUWH4 submitted 2008-08-29 hep-th

Z. Bern , J. J. M. Carrasco , L. J. Dixon , H. Johansson , R. Roiban This is my paper · ORCID
classification hep-th
keywords amplitudethree-loopfour-pointbehaviorcancellationsquadraticsupergravityultraviolet
verification ladder T0 review T1 audit T2 compute T3 formal
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Using the method of maximal cuts, we obtain a form of the three-loop four-point scattering amplitude of 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 N=4 super-Yang-Mills theory. By direct integration we confirm that no additional cancellations remain in the 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 N=4 super-Yang-Mills theory.

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Cited by 4 Pith papers

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  3. Gravity loop integrands from the ultraviolet

    hep-th 2019-09 conditional novelty 7.0 of 10

    Four-dimensional N=8 supergravity loop integrands scale one power better at infinity than general-D power-counting predicts, and this homogeneous scaling combined with BCFW behavior uniquely fixes the integrand throug...

  4. Energy correlators in four-dimensional gravity

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    Gravitational energy correlators in four dimensions are computed at one loop, shown to be infrared-finite, and resummed in the back-to-back limit by soft-graviton exponentiation.

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