N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops

Abstract

We present the full two-loop four-graviton amplitudes in N=4,5,6 supergravity. These results were obtained using the double-copy structure of gravity, which follows from the recently conjectured color-kinematics duality in gauge theory. The two-loop four-gluon scattering amplitudes in N=0,1,2 supersymmetric gauge theory are a second essential ingredient. The gravity amplitudes have the expected infrared behavior: the two-loop divergences are given in terms of the squares of the corresponding one-loop amplitudes. The finite remainders are presented in a compact form. The finite remainder for N=8 supergravity is also presented, in a form that utilizes a pure function with a very simple symbol.

31 pages, 2 figures, 1 table. v2: minor corrections, and references added

References in corpus (32)

• New Relations for Gauge-Theory Amplitudes
• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Minimal Basis for Gauge Theory Amplitudes
• Bootstrapping the three-loop hexagon
• Three-Loop Superfiniteness of N=8 Supergravity
• The Kinematic Algebra From the Self-Dual Sector
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• E7(7) constraints on counterterms in N=8 supergravity
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Taming Tree Amplitudes In General Relativity
• Collinear and Soft Divergences in Perturbative Quantum Gravity
• The No-Triangle Hypothesis for N=8 Supergravity
• A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
• Stringy KLT relations, global symmetries, and E_7(7) violation
• On duality symmetries of supergravity invariants
• E7(7) symmetry in perturbatively quantised N=8 supergravity
• High energy scattering in gravity and supergravity
• Two-loop graviton scattering relation and IR behavior in N=8 supergravity
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• Note on graviton MHV amplitudes
• On Cancellations of Ultraviolet Divergences in Supergravity Amplitudes
• On KLT and SYM-supergravity relations from 5-point 1-loop amplitudes
• On-shell recursion relations for gravity

Cited by in corpus (87)

• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• Pure Gravities via Color-Kinematics Duality for Fundamental Matter
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• Algebras for Amplitudes
• Double copy for massive quantum particles with spin
• Colour-Kinematics Duality for One-Loop Rational Amplitudes
• Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• Universality in the classical limit of massless gravitational scattering
• BCJ duality and the double copy in the soft limit
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Relationship Between Gravity and Gauge Scattering in the High Energy Limit
• Gravity Amplitudes as Generalized Double Copies
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• Integrand Oxidation and One-Loop Colour-Dual Numerators in N=4 Gauge Theory
• Effective action of dilaton gravity as the classical double copy of Yang-Mills theory
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity at subleading level
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• Double Copy from Homotopy Algebras
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Graviton-Photon Scattering
• Wilson line approach to gravity in the high energy limit
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• An algebraic approach to BCJ numerators
• Gravitational radiation from the classical spinning double copy
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
• BCJ duality and double copy in the closed string sector
• On the Double Copy for Spinning Matter
• Off-Shell Color-Kinematics Duality for Chern-Simons
• The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity
• Simple encoding of higher derivative gauge and gravity counterterms
• Unraveling conformal gravity amplitudes
• Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
• Color-Kinematics Duality in Multi-Regge Kinematics and Dimensional Reduction
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• Loop-Level Double-Copy for Massive Quantum Particles
• Conformal Gravity from Gauge Theory
• All-loop group-theory constraints for color-ordered SU(N) gauge-theory amplitudes
• The Two-Loop Four-Graviton Scattering Amplitudes
• SU(N) group-theory constraints on color-ordered five-point amplitudes at all loop orders
• Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
• Virtual Color-Kinematics Duality: 6-pt 1-Loop MHV Amplitudes
• On Three-Algebra and Bi-Fundamental Matter Amplitudes and Integrability of Supergravity
• Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N}=4$ Super Yang-Mills and $\mathcal{N}=8$ Supergravity
• Gauge $\times$ Gauge on Spheres
• Off-shell Currents and Color-Kinematics Duality
• Dual-color decompositions at one-loop level in Yang-Mills theory
• One-loop four-graviton amplitudes in N=4 supergravity models
• A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator
• Manifesting enhanced cancellations in supergravity: integrands versus integrals
• UV cancelations in gravity loop integrands
• The Complete KLT-Map Between Gravity and Gauge Theories
• Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Linear relations between N >= 4 supergravity and subleading-color SYM amplitudes
• KLT-type relations for QCD and bicolor amplitudes from color-factor symmetry
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• An Introduction to Webs
• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• The Classical Double Copy for Half-Maximal Supergravities and T-duality
• Color-kinematics duality and dimensional reduction for graviton emission in Regge limit
• Manifest colour-kinematics duality and double-copy in the string-based formalism
• The Construction of Dual-trace Factor in Yang-Mills Theory
• The gravitational cusp anomalous dimension from AdS space
• Note on Construction of Dual-trace Factor in Yang-Mills Theory
• Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation
• One-loop SYM-supergravity relation for five-point amplitudes
• Aspects of High Energy Scattering
• BCJ, worldsheet quantum algebra and KZ equations
• Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies
• Two-loop n-point anomalous amplitudes in N=4 supergravity
• Next-to-MHV Yang-Mills kinematic algebra
• Non-Abelian gauged supergravities as double copies
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• All-loop-orders relation between Regge limits of $\mathcal{N}=4$ SYM and $\mathcal{N}=8$ supergravity four-point amplitudes
• Quantum Gravity Needs Supersymmetry
• Double-logarithms in N=8 supergravity: impact parameter description and mapping to 1-rooted ribbon graphs
• Scattering amplitudes in gauge theories with and without supersymmetry
• Scattering Amplitudes in Gauge Theories
• Color-factor symmetry and BCJ relations for QCD amplitudes