Two-loop graviton scattering relation and IR behavior in N=8 supergravity

Abstract

We derive an ABDK-like relation between the one- and two-loop four-graviton amplitudes in N=8 supergravity. Specifically we show that the infrared divergent part of the two-loop amplitude is one-half the square of the one-loop amplitude, suggesting an exponential structure for IR divergences. The difference between the two-loop amplitude and one-half the square of the full one-loop amplitude is therefore finite, and expressible in a relatively simple form. We give arguments for generalizations to higher loops and n-point functions, suggesting that the exponential of the full one-loop amplitude may be corrected, to low orders, by only simple finite terms.

19 pages; v2: reference added; v3, published version: slight change in conventions, minor comments, added reference

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Cited by in corpus (38)

• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• Universality in the classical limit of massless gravitational scattering
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• Bootstrapping the QCD soft anomalous dimension
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• The three-loop form factor in N=4 super Yang-Mills
• Four-gluon scattering at three loops, infrared structure and Regge limit
• The Tree Formula for MHV Graviton Amplitudes
• Eikonal methods applied to gravitational scattering amplitudes
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity
• Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity at subleading level
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Wilson line approach to gravity in the high energy limit
• N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
• On the renormalization of multiparton webs
• All-loop infrared-divergent behavior of most-subleading-color gauge-theory amplitudes
• Angular momentum of zero-frequency gravitons
• The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity
• Infrared Divergences and the Eikonal Exponentiation
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• Tree-Level Amplitudes in N=8 Supergravity
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• The Two-Loop Four-Graviton Scattering Amplitudes
• N=8 Supergravity on the Light Cone
• Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N}=4$ Super Yang-Mills and $\mathcal{N}=8$ Supergravity
• UV cancelations in gravity loop integrands
• Linear relations between N >= 4 supergravity and subleading-color SYM amplitudes
• A super MHV vertex expansion for N=4 SYM theory
• IR divergences and Regge limits of subleading-color contributions to the four-gluon amplitude in N=4 SYM Theory
• The Full-Color Two-Loop Four-Gluon Amplitude in $\mathcal{N}=2$ Super-QCD
• On KLT and SYM-supergravity relations from 5-point 1-loop amplitudes
• Deviation from Alday-Maldacena Duality For Wavy Circle
• Applications of Subleading-color Amplitudes in N=4 SYM Theory
• Two-loop Doubly Massive Four-Point Amplitude Involving a half-BPS and Konishi Operator
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• All-loop-orders relation between Regge limits of $\mathcal{N}=4$ SYM and $\mathcal{N}=8$ supergravity four-point amplitudes
• A Note on Loop Amplitudes in QED