Four-point Amplitudes in N=8 Supergravity and Wilson Loops

Abstract

Prompted by recent progress in the study of N=4 super Yang-Mills amplitudes, and evidence that similar approaches might be relevant to N=8 supergravity, we investigate possible iterative structures and applications of Wilson loop techniques in maximal supergravity. We first consider the two-loop, four-point MHV scattering amplitude in N=8 supergravity, confirming that the infrared divergent parts exponentiate, and we give the explicit expression which represents the failure for this to occur for the finite part. We observe that each term in the expansion of the one- and two-loop amplitudes in the dimensional regularisation parameter epsilon has a uniform degree of transcendentality. We then turn to consider Wilson loops in supergravity, showing that a natural definition of the loop, involving the Christoffel connection, fails to reproduce the one-loop amplitude. An alternative expression, which involves the metric explicitly, is shown to have a close relationship with the physical amplitude. We find that in a gauge in which the cusp diagrams vanish, the remaining diagrams for this Wilson loop correctly generate the full one-loop, four-point N=8 supergravity amplitude.

32 pages, 4 figures. v2: typos corrected. v3: Clarifications added in section 3, typos fixed. Published version to appear in Nuclear Physics B

References in corpus (47)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Harmonic Polylogarithms
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Gluon scattering amplitudes at strong coupling
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Transcendentality and Crossing
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• Wilson Loops and Minimal Surfaces
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Magic identities for conformal four-point integrals
• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang-Mills model
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• On planar gluon amplitudes/Wilson loops duality
• HPL, a Mathematica implementation of the harmonic polylogarithms
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Multi-loop Amplitudes and Resummation
• Analytical Result for Dimensionally Regularized Massless On-shell Double Box
• Comments on gluon scattering amplitudes via AdS/CFT
• Non-planar massless two-loop Feynman diagrams with four on-shell legs
• Hexagon Wilson loop = six-gluon MHV amplitude
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Three-Loop Superfiniteness of N=8 Supergravity
• One-Loop Self-Dual and N=4 Super Yang-Mills
• Eikonal Quantum Gravity and Planckian Scattering
• Perturbative Quantum Gravity and its Relation to Gauge Theory
• Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• Is N = 8 Supergravity Ultraviolet Finite?
• Calculation of Graviton Scattering Amplitudes using String-Based Methods
• Extension of HPL to complex arguments
• Ultraviolet properties of Maximal Supergravity
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Unexpected Cancellations in Gravity Theories
• The No-Triangle Hypothesis for N=8 Supergravity
• Planckian Energy Scattering and Surface Terms in the Gravitational Action
• From Trees to Loops and Back
• Gauge Invariance and Anomalous Dimensions of a Light-Cone Wilson Loop in Light-Like Axial Gauge
• Two-loop graviton scattering relation and IR behavior in N=8 supergravity
• Cusped SYM Wilson loop at two loops and beyond
• Wilson loops in four-dimensional quantum gravity
• On the finiteness of N=8 quantum supergravity
• One-loop N=8 Supergravity Amplitudes from MHV Diagrams
• Worldlines as Wilson Lines

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• A super MHV vertex expansion for N=4 SYM theory
• Gravitational Wilson Loop in Discrete Quantum Gravity
• The gravitational cusp anomalous dimension from AdS space
• Quantization Conditions and the Double Copy
• Observations on Open and Closed String Scattering Amplitudes at High Energies
• The Full-Color Two-Loop Four-Gluon Amplitude in $\mathcal{N}=2$ Super-QCD
• MHV amplitudes in N=2 SQCD and in N=4 SYM at one loop
• Soft collinear effective theory for gravity
• $\mathcal{N}=7$ On-Shell Diagrams and Supergravity Amplitudes in Momentum Twistor Space
• Holonomies of gauge fields in twistor space 2: Hecke algebra, diffeomorphism, and graviton amplitudes
• Applications of Subleading-color Amplitudes in N=4 SYM Theory
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• 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
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