Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity

Abstract

Using the method of maximal cuts, we obtain a form of the three-loop four-point scattering amplitude of N=8 supergravity in which all ultraviolet cancellations are made manifest. The Feynman loop integrals that appear have a graphical representation with only cubic vertices, and numerator factors that are quadratic in the loop momenta, rather than quartic as in the previous form. This quadratic behavior reflects cancellations beyond those required for finiteness, and matches the quadratic behavior of the three-loop four-point scattering amplitude in N=4 super-Yang-Mills theory. By direct integration we confirm that no additional cancellations remain in the N=8 supergravity amplitude, thus demonstrating that the critical dimension in which the first ultraviolet divergence occurs at three loops is D_c=6. We also give the values of the three-loop divergences in D=7,9,11. In addition, we present the explicitly color-dressed three-loop four-point amplitude of N=4 super-Yang-Mills theory.

arXiv comment38 pages, 10 figures, 3 tables

References in corpus (82)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• New Relations for Gauge-Theory Amplitudes
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• New Recursion Relations for Tree Amplitudes of Gluons
• Gluon scattering amplitudes at strong coupling
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• Magic identities for conformal four-point integrals
• One-Loop Amplitudes for e^+ e^- to Four Partons
• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• New Color Decompositions for Gauge Amplitudes at Tree and Loop Level
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Multi-loop Amplitudes and Resummation
• Comments on gluon scattering amplitudes via AdS/CFT
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Massive Loop Amplitudes from Unitarity
• Evolution of Color Exchange in QCD Hard Scattering
• On Tree Amplitudes in Gauge Theory and Gravity
• Progress in One-Loop QCD Computations
• One loop in eleven dimensions
• Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
• Three-Loop Superfiniteness of N=8 Supergravity
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• One-Loop Self-Dual and N=4 Super Yang-Mills
• Two-Loop g -> gg Splitting Amplitudes in QCD
• Perturbative Quantum Gravity and its Relation to Gauge Theory
• Duality and higher derivative terms in M theory
• Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit
• Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts
• Universal structure of subleading infrared poles in gauge theory amplitudes
• Two loops in eleven dimensions
• The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
• Threshold Resummation for Dijet Cross Sections
• Is N = 8 Supergravity Ultraviolet Finite?
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• All Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory
• Calculation of Graviton Scattering Amplitudes using String-Based Methods
• A Two-Loop Four-Gluon Helicity Amplitude in QCD
• Low energy expansion of the four-particle genus-one amplitude in type II superstring theory
• Resummed event shapes at hadron-hadron colliders
• Ultraviolet properties of Maximal Supergravity
• Non-MHV Tree Amplitudes in Gauge Theory
• Taming Tree Amplitudes In General Relativity
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• On the Coupling of Gravitons to Matter
• Unexpected Cancellations in Gravity Theories
• Perturbative Gravity from QCD Amplitudes
• Inherited Twistor-Space Structure of Gravity Loop Amplitudes
• Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity
• New Higher-Derivative $R^4$ Theorems
• The No-Triangle Hypothesis for N=8 Supergravity
• Supersymmetry counterterms revisited
• Two-Loop Amplitudes of Gluons and Octa-Cuts in N=4 Super Yang-Mills
• MHV-Vertices for Gravity Amplitudes
• Infinities within graviton scattering amplitudes
• Absence of Triangles in Maximal Supergravity Amplitudes
• Decoupling Supergravity from the Superstring
• KLT relations from the Einstein-Hilbert Lagrangian
• Iterative Structure Within The Five-Particle Two-Loop Amplitude
• Six-Point One-Loop N=8 Supergravity NMHV Amplitudes and their IR behaviour
• Modular properties of two-loop maximal supergravity and connections with string theory
• Simplifying Algebra in Feynman Graphs, Part II: Spinor Helicity from the Spacecone
• Analytical Result for Dimensionally Regularized Massless On-Shell Planar Triple Box
• Explicit Action of E7(7) on N=8 Supergravity Fields
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• String theory and the mapping of gravity into gauge theory
• Two-loop graviton scattering relation and IR behavior in N=8 supergravity
• Note on graviton MHV amplitudes
• Explicit Cancellation of Triangles in One-loop Gravity Amplitudes
• Lectures on multiloop calculations
• E_7(7) on the Light Cone
• Generalized string theory mapping relations between gravity and gauge theory
• QCD recursion relations from the largest time equation
• Recursion Relations for One-Loop Gravity Amplitudes
• On Cancellations of Ultraviolet Divergences in Supergravity Amplitudes
• On-shell recursion relations for gravity

Cited by in corpus (123)

• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• Infrared singularities of scattering amplitudes in perturbative QCD
• The Ultraviolet Behavior of N=8 Supergravity at Four Loops
• Lorentz symmetry breaking as a quantum field theory regulator
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Towards a Basis for Planar Two-Loop Integrals
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
• The S-Matrix in Twistor Space
• The Ultraviolet Properties of N=4 Supergravity at Four Loops
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• E7(7) constraints on counterterms in N=8 supergravity
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
• Basics of Generalized Unitarity
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
• On soft singularities at three loops and beyond
• Maximal Unitarity at Two Loops
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• Automorphic properties of low energy string amplitudes in various dimensions
• The infrared structure of gauge theory amplitudes in the high-energy limit
• Generalized Unitarity and Six-Dimensional Helicity
• Gravity Amplitudes as Generalized Double Copies
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• The vanishing volume of D=4 superspace
• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• A simple approach to counterterms in N=8 supergravity
• Stringy KLT relations, global symmetries, and E_7(7) violation
• Four-gluon scattering at three loops, infrared structure and Regge limit
• The Tree Formula for MHV Graviton Amplitudes
• Generic multiloop methods and application to N=4 super-Yang-Mills
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• How Far Are We from the Quantum Theory of Gravity?
• Equivalent D=3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories
• Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Solution to the Ward Identities for Superamplitudes
• R^4 counterterm and E7(7) symmetry in maximal supergravity
• Integrability of Black Hole Orbits in Maximal Supergravity
• Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• Duals of Feynman Integrals, I: Differential Equations
• N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• An algebraic approach to BCJ numerators
• Tropical Amplitudes
• The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
• All-loop infrared-divergent behavior of most-subleading-color gauge-theory amplitudes
• BCJ duality and double copy in the closed string sector
• Two-Loop Maximal Unitarity with External Masses
• Matter Dependence of the Three-Loop Soft Anomalous Dimension Matrix
• Covariant procedures for perturbative non-linear deformation of duality-invariant theories
• On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts
• Loops in exceptional field theory
• Amplitudes and Ultraviolet Behavior of N=8 Supergravity
• Superconformal symmetry and maximal supergravity in various dimensions
• Tree-Level Amplitudes in N=8 Supergravity
• Simplicity in the Structure of QED and Gravity Amplitudes
• $D^6{R}^4$ amplitudes in various dimensions
• Poisson equation for the Mercedes diagram in string theory at genus one
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• Unraveling L_{n,k}: Grassmannian Kinematics
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• Susy Theories and QCD: Numerical Approaches
• Covariant actions for models with non-linear twisted self-duality
• N=8 Supergravity 4-point Amplitudes
• N=8 Supergravity on the Light Cone
• N=2 Supersymmetry and U(1)-Duality
• Generalized unitarity and the worldsheet S matrix in AdS_n x S^n x M^(10-2n)
• Maximal Unitarity for the Four-Mass Double Box
• Spectrum Generating Conformal and Quasiconformal U-Duality Groups, Supergravity and Spherical Vectors
• SUSY Ward identities, Superamplitudes, and Counterterms
• Higher Derivative Supergravities in Diverse Dimensions
• One-loop four-graviton amplitudes in N=4 supergravity models
• New E77 invariants and amplitudes
• Higher-loop amplitudes in the non-minimal pure spinor formalism
• Building Bases of Loop Integrands
• On UV Finiteness of the Four Loop N=8 Supergravity
• Gravitino Interactions from Yang-Mills Theory
• Non-planarity through unitarity in ABJM
• Perturbative expansion of N<8 Supergravity
• A super MHV vertex expansion for N=4 SYM theory
• Cross-Order Integral Relations from Maximal Cuts
• The D^6 R^4 term from three loop maximal supergravity
• IR divergences and Regge limits of subleading-color contributions to the four-gluon amplitude in N=4 SYM Theory
• Review of AdS/CFT Integrability, Chapter V.1: Scattering Amplitudes - a Brief Introduction
• Cancellation of divergences up to three loops in exceptional field theory
• The Structure of Multiloop Amplitudes in Gauge and Gravity Theories
• Minimal unitary representation of SO*(8) = SO(6,2) and its SU(2) deformations as massless 6D conformal fields and their supersymmetric extensions
• One-loop SYM-supergravity relation for five-point amplitudes
• Gravity loop integrands from the ultraviolet
• Relations Between Closed String Amplitudes at Higher-order Tree Level and Open String Amplitudes
• Constitutive relations, off shell duality rotations and the hypergeometric form of Born-Infeld theory
• Pair Production of small Black Holes in Heterotic String Theories
• Perturbative type II amplitudes for BPS interactions
• Supersymmetry constraints on U-duality invariant deformations of $N\ge 5$ Supergravity
• Disk relations for tree amplitudes in minimal coupling theory of gauge field and gravity
• A Note on Single Soft Scalar Emission of $\mathcal{N}=8$ SUGRA and $E_{7(7)}$ Symmetry
• Applications of Subleading-color Amplitudes in N=4 SYM Theory
• String theory integrands and supergravity divergences
• Local integrands for the five-point amplitude in planar N=4 SYM up to five loops
• Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes
• Generalizing the ADM Computation to Quantum Field Theory
• Illustrations of Integrand-Basis Building at Two Loops
• Pure spinor indications of ultraviolet finiteness in D=4 maximal supergravity
• Obstruction to E_{7(7)} Deformation in N=8 Supergravity
• 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
• Non-analytic terms of string amplitudes from partial waves
• On the non-planar beta-deformed N=4 super-Yang-Mills theory
• Non--analytic terms from nested divergences in maximal supergravity
• Constraining non--BPS interactions from counterterms in three loop maximal supergravity
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Instanton corrections to the effective action of N=4 SYM
• Do Three Dimensions tell us Anything about a Theory of Everything?
• Jet Physics from Static Charges in AdS
• Exceptional symmetries in light-cone superspace
• A Master Action for D=11 Supergravity in the Component Formulation
• Some finite terms from ladder diagrams in three and four loop maximal supergravity