A tale of two exponentiations in $\mathcal{N}=8$ supergravity at subleading level

Abstract

High-energy massless gravitational scattering in $\mathcal{N}=8$ supergravity was recently analyzed at leading level in the deflection angle, uncovering an interesting connection between exponentiation of infrared divergences in momentum space and the eikonal exponentiation in impact parameter space. Here we extend that analysis to the first non trivial sub-leading level in the deflection angle which, for massless external particles, implies going to two loops, i.e. to third post-Minkowskian (3PM) order. As in the case of the leading eikonal, we see that the factorisation of the momentum space amplitude into the exponential of the one-loop result times a finite remainder hides some basic simplicity of the impact parameter formulation. For the conservative part of the process, the explicit outcome is infrared (IR) finite, shows no logarithmic enhancement, and agrees with an old claim in pure Einstein gravity, while the dissipative part is IR divergent and should be regularized, as usual, by including soft gravitational bremsstrahlung. Finally, using recent three-loop results, we test the expectation that eikonal formulation accounts for the exponentiation of the lower-loop results in the momentum space amplitude. This passes a number of highly non-trivial tests, but appears to fail for the dissipative part of the process at all loop orders and sufficiently subleading order in $\epsilon$, hinting at some lack of commutativity of the relevant infrared limits for each exponentiation.

arXiv comment37 pages

References in corpus (45)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• Effective one-body approach to general relativistic two-body dynamics
• Transition from inspiral to plunge in binary black hole coalescences
• Dimensionally Regulated Pentagon Integrals
• Coalescence of Two Spinning Black Holes: An Effective One-Body Approach
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• Amplitudes, Observables, and Classical Scattering
• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• High-energy gravitational scattering and the general relativistic two-body problem
• General Relativity from Scattering Amplitudes
• From Boundary Data to Bound States
• Eikonal Quantum Gravity and Planckian Scattering
• A Numerical Relativity Waveform Surrogate Model for Generically Precessing Binary Black Hole Mergers
• Scattering at Planckian Energies
• Factorization Properties of Soft Graviton Amplitudes
• Revisiting the 2PM eikonal and the dynamics of binary black holes
• Calculation of Graviton Scattering Amplitudes using String-Based Methods
• Classical and Quantum Results on Logarithmic Terms in the Soft Theorem in Four Dimensions
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• Light-like Scattering in Quantum Gravity
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• The infrared structure of gauge theory amplitudes in the high-energy limit
• Towards an S-matrix Description of Gravitational Collapse
• Next-to-soft corrections to high energy scattering in QCD and gravity
• Infrared features of gravitational scattering and radiation in the eikonal approach
• Eikonal methods applied to gravitational scattering amplitudes
• Observational Signature of the Logarithmic Terms in the Soft Graviton Theorem
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity
• Integrability of Black Hole Orbits in Maximal Supergravity
• Wilson line approach to gravity in the high energy limit
• Two-parton scattering in the high-energy limit
• An infrared approach to Reggeization
• Unified limiting form of graviton radiation at extreme energies
• High-energy string-brane scattering: leading eikonal and beyond
• Two-loop graviton scattering relation and IR behavior in N=8 supergravity
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• The Subleading Eikonal in Supergravity Theories
• Soft gravitational radiation from ultra-relativistic collisions at sub- and sub-sub-leading order
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• Infrared singularities of QCD scattering amplitudes in the Regge limit to all orders
• Microscopic unitary description of tidal excitations in high-energy string-brane collisions
• Gravitino one-loop contribution to Planckian Scattering
• Eikonal Scattering in Kaluza-Klein Gravity

Cited by in corpus (51)

• Classical black hole scattering from a worldline quantum field theory
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• Classical and quantum scattering in post-Minkowskian gravity
• Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory
• The Eikonal Approach to Gravitational Scattering and Radiation at $\mathcal{O}(G^3)$
• Radiative contribution to classical gravitational scattering at the third order in $G$
• Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
• Universality of ultra-relativistic gravitational scattering
• Gravitational Bremsstrahlung from Reverse Unitarity
• Radiation Reaction from Soft Theorems
• Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
• Gravitational Bremsstrahlung in the Post-Minkowskian Effective Field Theory
• SUSY in the Sky with Gravitons
• Tidal Effects in the Post-Minkowskian Expansion
• Sixth post-Newtonian nonlocal-in-time dynamics of binary systems
• Classical Gravitational Scattering at $\mathcal{O}(G^3)$ from Feynman Diagrams
• On an Exponential Representation of the Gravitational S-Matrix
• Classical Gravity from Loop Amplitudes
• Radiative contributions to gravitational scattering
• Second-order Post-Minkowskian scattering in arbitrary dimensions
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• Quadratic-in-Spin Hamiltonian at $\mathcal{O}(G^2)$ from Scattering Amplitudes
• Compton Black-Hole Scattering for $s\le 5/2$
• Testing binary dynamics in gravity at the sixth post-Newtonian level
• Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory
• High Energy Scattering in Perturbative Quantum Gravity at Next to Leading Power
• Classical Solutions and their Double Copy in Split Signature
• Strong-field scattering of two black holes: Numerical Relativity meets Post-Minkowskian gravity
• Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
• Scattering of tidally interacting bodies in post-Minkowskian gravity
• Mining the Geodesic Equation for Scattering Data
• Gravitational bremsstrahlung from spinning binaries in the post-Minkowskian expansion
• Angular momentum of zero-frequency gravitons
• Infrared Divergences and the Eikonal Exponentiation
• Gravitational Bremsstrahlung with tidal effects in the post-Minkowskian expansion
• Eikonal amplitudes from curved backgrounds
• Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model
• Gravitational Regge bounds
• Light bending from eikonal in worldline quantum field theory
• Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N}=4$ Super Yang-Mills and $\mathcal{N}=8$ Supergravity
• Where is M-theory in the space of scattering amplitudes?
• Generalizing event shapes: In search of lost collider time
• Classical and quantum gravitational scattering with Generalized Wilson Lines
• Large Gauge Effects and the Structure of Amplitudes
• Quantization Conditions and the Double Copy
• Strong Field Scattering of Black Holes: Assessing Resummation Strategies
• All-loop-orders relation between Regge limits of $\mathcal{N}=4$ SYM and $\mathcal{N}=8$ supergravity four-point amplitudes
• Gravitational scattering of two neutron stars
• Strong Field Scattering of Two Black Holes: Exploring Gauge Flexibility
• Yang-Mills observables: from KMOC to eikonal through EFT
• The Radial Action from Probe Amplitudes to All Orders