The critical ultraviolet behaviour of N=8 supergravity amplitudes

Abstract

We analyze the critical ultraviolet behaviour of the four-graviton amplitude in N=8 supergravity to all order in perturbation. We use the Bern-Carrasco-Johansson diagrammatic expansion for N=8 supergravity multiloop amplitudes, where numerator factors are squares of the Lorentz factor of N=4 super-Yang-Mills amplitudes, and the analysis of the critical ultraviolet behaviour of the multiloop four-gluon amplitudes in the single- and double-trace sectors. We argue this implies that the superficial ultraviolet behaviour of the four-graviton N=8 amplitudes from four-loop order is determined by the factorization the k^8 R^4 operator. This leads to a seven-loop logarithmic divergence in the four-graviton amplitude in four dimensions.

latex. 5 pages. v2: Added references and minor changes

References in corpus (6)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• Three-Loop Superfiniteness of N=8 Supergravity
• Ultraviolet properties of Maximal Supergravity
• New Higher-Derivative $R^4$ Theorems
• Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization

Cited by in corpus (11)

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• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• Amplitudes at Infinity
• Arguments Against a Finite N=8 Supergravity
• Challenges of D=6 N=(1,1) SYM Theory
• Perturbative Gravity and Gauge Theory Relations -- A Review
• Scattering amplitudes in gauge theories with and without supersymmetry
• Infrared Finite Observables in N=8 Supergravity
• Perturbative and Non-Perturbative Aspects of N=8 Supergravity