On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences

Abstract

String theory implies that field theories containing gravity are in a certain sense `products' of gauge theories. We make this product structure explicit up to two loops for the relatively simple case of N=8 supergravity four-point amplitudes, demonstrating that they are `squares' of N=4 super-Yang-Mills amplitudes. This is accomplished by obtaining an explicit expression for the $D$-dimensional two-loop contribution to the four-particle S-matrix for N=8 supergravity, which we compare to the corresponding N=4 Yang-Mills result. From these expressions we also obtain the two-loop ultraviolet divergences in dimensions D=7 through D=11. The analysis relies on the unitarity cuts of the two theories, many of which can be recycled from a one-loop computation. The two-particle cuts, which may be iterated to all loop orders, suggest that squaring relations between the two theories exist at any loop order. The loop-momentum power-counting implied by our two-particle cut analysis indicates that in four dimensions the first four-point divergence in N=8 supergravity should appear at five loops, contrary to the earlier expectation, based on superspace arguments, of a three-loop counterterm.

Latex, 52 pages, discussion of 2 loop divergences in D=8,10 added

References in corpus (6)

• Multi-Parton Amplitudes in Gauge Theories
• One-Loop Amplitudes for e^+ e^- to Four Partons
• One loop in eleven dimensions
• Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
• One-Loop Self-Dual and N=4 Super Yang-Mills
• One-loop four-graviton amplitude in eleven-dimensional supergravity

Cited by in corpus (330)

• New Relations for Gauge-Theory Amplitudes
• Gluon scattering amplitudes at strong coupling
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Dilaton Gravity in Two Dimensions
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• Quantum Gravity: a Progress Report
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Gravity as the Square of Gauge Theory
• New Color Decompositions for Gauge Amplitudes at Tree and Loop Level
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Black holes and the double copy
• Non-planar massless two-loop Feynman diagrams with four on-shell legs
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• A Duality For The S Matrix
• The Ultraviolet Behavior of N=8 Supergravity at Four Loops
• Three-Loop Superfiniteness of N=8 Supergravity
• The Infrared Behavior of One-Loop Gluon Amplitudes at Next-to-Next-to-Leading Order
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• The classical double copy for Taub-NUT spacetime
• The Infrared Behavior of One-Loop QCD Amplitudes at Next-to-Next-to-Leading Order
• M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills
• On D=5 super Yang-Mills theory and (2,0) theory
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Two-Loop g -> gg Splitting Amplitudes in QCD
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• Perturbative Quantum Gravity and its Relation to Gauge Theory
• Duality and higher derivative terms in M theory
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts
• Two-Loop Helicity Amplitudes for Gluon-Gluon Scattering in QCD and Supersymmetric Yang-Mills Theory
• Two-loop Integrand Decomposition into Master Integrals and Surface Terms
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• Two loops in eleven dimensions
• On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring
• Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
• Is N = 8 Supergravity Ultraviolet Finite?
• The S-Matrix in Twistor Space
• Factorization Properties of Soft Graviton Amplitudes
• Gravitational S-matrix from CFT dispersion relations
• Bootstrapping Multi-Parton Loop Amplitudes in QCD
• The Ultraviolet Properties of N=4 Supergravity at Four Loops
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• The Cut-Constructible Part of QCD Amplitudes
• All Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• Low energy expansion of the four-particle genus-one amplitude in type II superstring theory
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• The Kerr-Schild double copy in curved spacetime
• Color-kinematic Duality for Form Factors
• Supersymmetric higher-derivative actions in ten and eleven dimensions, the associated superalgebras and their formulation in superspace
• Colour-Kinematics Duality for One-Loop Rational Amplitudes
• 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
• Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N=4 SYM
• Ultraviolet properties of Maximal Supergravity
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• Two-Loop Correction to Bhabha Scattering
• On the Coupling of Gravitons to Matter
• On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
• Universality in the classical limit of massless gravitational scattering
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• Unexpected Cancellations in Gravity Theories
• 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
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• Classical Gravity from Loop Amplitudes
• Perturbative Gravity from QCD Amplitudes
• Gravity and Yang-Mills Amplitude Relations
• Scattering Amplitudes
• Automorphic properties of low energy string amplitudes in various dimensions
• Inherited Twistor-Space Structure of Gravity Loop Amplitudes
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• Where is String Theory?
• Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity
• Sharpening The Leading Singularity
• Worldline formalism in a gravitational background
• Two-Loop Helicity Amplitudes for Quark-Gluon Scattering in QCD and Gluino-Gluon Scattering in Supersymmetric Yang-Mills Theory
• String theory dualities and supergravity divergences
• The No-Triangle Hypothesis for N=8 Supergravity
• New Higher-Derivative $R^4$ Theorems
• Generalized Unitarity and Six-Dimensional Helicity
• Supersymmetry counterterms revisited
• Supertwistor space for 6D maximal super Yang-Mills
• Recursive Calculation of One-Loop QCD Integral Coefficients
• One-Loop Gluon Scattering Amplitudes in Theories with $N<4$ Supersymmetries
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• Two-Loop Helicity Amplitudes for Quark-Quark Scattering in QCD and Gluino-Gluino Scattering in Supersymmetric Yang-Mills Theory
• Evidence for a Nonplanar Amplituhedron
• A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
• Gravity, Twistors and the MHV Formalism
• 5 loops in 24/5 dimensions
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• The vanishing volume of D=4 superspace
• Exact solutions for the biadjoint scalar field
• A simple approach to counterterms in N=8 supergravity
• MHV-Vertices for Gravity Amplitudes
• Four-gluon scattering at three loops, infrared structure and Regge limit
• Eikonal methods applied to gravitational scattering amplitudes
• Generic multiloop methods and application to N=4 super-Yang-Mills
• BCJ numerators from reduced Pfaffian
• Prescriptive Unitarity
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• The ultra-violet question in maximally supersymmetric field theories
• How Far Are We from the Quantum Theory of Gravity?
• On the U(1) duality anomaly and the S-matrix of N=4 supergravity
• S-duality and the Double Copy
• Inelastic Exponentiation and Classical Gravitational Scattering at One Loop
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity
• Construction of an asymptotic S matrix for perturbative quantum gravity
• Gauge Theories from Orientifolds and Large N Limit
• Evanescent Effects Can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity at subleading level
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• The on-shell massless planar double box diagram with an irreducible numerator
• Double Copy from Homotopy Algebras
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• New Identities among Gauge Theory Amplitudes
• Two-loop corrections to Light-by-Light scattering in Supersymmetric QED
• Topology and Wilson lines: global aspects of the double copy
• The M-Theory S-Matrix From ABJM: Beyond 11D Supergravity
• One-Loop n-Point Helicity Amplitudes in (Self-Dual) Gravity
• Integrability of Black Hole Orbits in Maximal Supergravity
• R^4 counterterm and E7(7) symmetry in maximal supergravity
• Wilson line approach to gravity in the high energy limit
• N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• Higher-loop amplitude monodromy relations in string and gauge theory
• Six-Point One-Loop N=8 Supergravity NMHV Amplitudes and their IR behaviour
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• Dimensional regularization for N=1 susy sigma models and the worldline formalism
• Simple superamplitudes in higher dimensions
• Amplitudes in the beta-deformed Conformal Yang-Mills
• An algebraic approach to BCJ numerators
• Double-Copy Constructions and Unitarity Cuts
• The Double Pentaladder Integral to All Orders
• Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
• The D^4 R^4 term in type IIB string theory on T^2 and U-duality
• Tropical Amplitudes
• Expansion of All Multitrace Tree Level EYM Amplitudes
• High energy scattering in gravity and supergravity
• 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
• Weyl doubling
• BCJ duality and double copy in the closed string sector
• Twistor Space Structure of the Box Coefficients of N=1 One-loop Amplitudes
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• Counterterms/M-theory Corrections to D=11 Supergravity
• Large $p$ explorations. From SUGRA to big STRINGS in Mellin space
• Gauge and Gravity Amplitude Relations
• Monopoles, shockwaves and the classical double copy
• A note on the UV behaviour of maximally supersymmetric Yang-Mills theories
• Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory
• Regge behavior of gluon scattering amplitudes in N=4 SYM theory
• On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts
• Gravity On-shell Diagrams
• String theory and the mapping of gravity into gauge theory
• Biadjoint wires
• An Introduction to On-shell Recursion Relations
• Two-loop graviton scattering relation and IR behavior in N=8 supergravity
• Loops in exceptional field theory
• Amplitudes and Ultraviolet Behavior of N=8 Supergravity
• Amplitudes, Form Factors and the Dilatation Operator in $\mathcal{N}=4$ SYM Theory
• Tree Amplitudes and Two-loop Counterterms in D=11 Supergravity
• Tree-Level Amplitudes in N=8 Supergravity
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• Curvature invariants of static spherically symmetric geometries
• Explicit Cancellation of Triangles in One-loop Gravity Amplitudes
• Simplicity in the Structure of QED and Gravity Amplitudes
• Dual Conformal Symmetry, Integration-by-Parts Reduction, Differential Equations and the Nonplanar Sector
• Exploring transcendentality in superstring amplitudes
• Constraining Higher Derivative Supergravity with Scattering Amplitudes
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• Unraveling L_{n,k}: Grassmannian Kinematics
• On the structure of scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity
• Three-Loop Yang-Mills beta-Function via the Covariant Background Field Method
• Anomalies and divergences in N=4 supergravity
• Invariants and divergences in half-maximal supergravity theories
• Graviton Loop Corrections to Vacuum Polarization in de Sitter in a General Covariant Gauge
• Supersymmetric Ward Identities and NMHV Amplitudes involving Gluinos
• The Two-Loop Four-Graviton Scattering Amplitudes
• Generalized string theory mapping relations between gravity and gauge theory
• E_7(7) on the Light Cone
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• String Theory and Noncommutative Field Theories at One Loop
• On powercounting in perturbative quantum gravity theories through color-kinematic duality
• Superstring loop amplitudes from the field theory limit
• All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
• N=8 Supergravity on the Light Cone
• N=8 Supergravity 4-point Amplitudes
• 6d (2,0) and M-theory at 1-loop
• Virtuous Trees at Five and Six Points for Yang-Mills and Gravity
• Two-loop superstring five-point amplitudes II: Low energy expansion and S-duality
• Eleven-Dimensional Supergravity in Light-Cone Superspace
• KLT and New Relations for N=8 SUGRA and N=4 SYM
• Conformal Supergravity Tree Amplitudes from Open Twistor String Theory
• Integral invariants in maximally supersymmetric Yang-Mills theories
• Scattering amplitudes in strongly coupled N=4 SYM from semiclassical strings in AdS
• Supersymmetry, holonomy and Kundt spacetimes
• Two-loop $\mathcal{N}=2$ SQCD amplitudes with external matter from iterated cuts
• All loop structures in Supergravity Amplitudes on $Ad{S}_5\times S^5$ from CFT
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• The critical ultraviolet behaviour of N=8 supergravity amplitudes
• Higher Derivative Supergravities in Diverse Dimensions
• More on the Classical Double Copy in Three Spacetime Dimensions
• Full-color three-loop three-point form factors in N=4 SYM
• UV cancelations in gravity loop integrands
• Manifesting enhanced cancellations in supergravity: integrands versus integrals
• Correlation functions of local composite operators from generalized unitarity
• Spinor helicity structures in higher spin theories
• Soft theorems in maximally supersymmetric theories
• Observations on Arithmetic Invariants and U-Duality Orbits in N =8 Supergravity
• Two-loop five-point amplitudes of super Yang-Mills and supergravity in pure spinor superspace
• On Cancellations of Ultraviolet Divergences in Supergravity Amplitudes
• The Unitarity Method using a Canonical Basis Approach
• A remark on quantum gravity
• Perturbative Relations between Gravity and Gauge Theory
• Expansion of Einstein-Yang-Mills theory by Differential Operators
• Linear relations between N >= 4 supergravity and subleading-color SYM amplitudes
• Towards All Loop Supergravity Amplitudes on $Ad{S}_5\times S^5$
• The D^6 R^4 term in type IIB string theory on T^2 and U-duality
• Perturbative expansion of N<8 Supergravity
• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• Gravitino Interactions from Yang-Mills Theory
• Loop amplitudes in maximal supergravity with manifest supersymmetry
• Graviton emission in Einstein-Hilbert gravity
• Non-planarity through unitarity in ABJM
• A Note on Graviton Amplitudes for New Twistor String Theories
• Infinities in Quantum Gravities
• Extracting Einstein from the Loop-Level Double-Copy
• Scalar field theory limits of bosonic string amplitudes
• Gravity and Form Scattering and Renormalisation of Gravity in Six and Eight Dimensions
• Lorentzian manifolds and scalar curvature invariants
• Eleven dimensional supergravity in light cone gauge
• The D^6 R^4 term from three loop maximal supergravity
• On tree amplitudes with gluons coupled to gravitons
• Supervertices and Non-renormalization Conditions in Maximal Supergravity Theories
• S and U-duality Constraints on IIB S-matrices
• On a possibility of a UV finite N=8 supergravity
• Review of AdS/CFT Integrability, Chapter V.1: Scattering Amplitudes - a Brief Introduction
• Reggeization of N=8 Supergravity and N=4 Yang-Mills Theory II
• One-loop corrections to the D3 brane action
• Scattering on the Moduli Space of N=4 Super Yang-Mills
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Note on symmetric BCJ numerator
• Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation
• The Structure of Multiloop Amplitudes in Gauge and Gravity Theories
• Type II and heterotic one loop string effective actions in four dimensions
• Graviton-Form Invariants in D=11 Supergravity
• One-loop SYM-supergravity relation for five-point amplitudes
• Hidden Conformal Symmetry in Tree-Level Graviton Scattering
• On the amplitudes in N=(1,1) D=6 SYM
• N=4 Super-Yang-Mills Theory, QCD and Collider Physics
• Dual expansions of N=4 super Yang-Mills theory via IIB superstring theory
• Gravity loop integrands from the ultraviolet
• Recent Progress in Perturbative Quantum Field Theory
• On Perturbative Gravity and Gauge Theory
• Challenges of D=6 N=(1,1) SYM Theory
• Hidden Beauty in Multiloop Amplitudes
• M-theory and automorphic scattering
• MHV amplitudes in N=2 SQCD and in N=4 SYM at one loop
• Relations Between Closed String Amplitudes at Higher-order Tree Level and Open String Amplitudes
• String Primer
• Pair Production of small Black Holes in Heterotic String Theories
• Not so non-renormalizable gravity
• 1/8-BPS Couplings and Exceptional Automorphic Functions
• Flavour-kinematics duality for Goldstone modes
• Two-Loop ${\varphi }^4$-Diagrams from String Theory
• Effective actions in $\mathcal{N}$=1, D5 supersymmetric gauge theories: harmonic superspace approach
• Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes
• Perturbative type II amplitudes for BPS interactions
• D3-Brane Loop Amplitudes from M5-Brane Tree Amplitudes
• Asymptotics of the $D^8{R}^4$ genus-two string invariant
• Ultraviolet divergences in maximal supergravity from a pure spinor point of view
• $\mathcal{E}{\nabla }^4{R}^4$ type invariants and their gradient expansion
• Applications of Subleading-color Amplitudes in N=4 SYM Theory
• Supersymmetric Yang-Mills and Supergravity Amplitudes at One Loop
• Two-Loop Diagrammatics in a Self-Dual Background
• The $\mathcal{N}=4$ Supergravity NMHV six-point one-loop amplitude
• Disk relations for tree amplitudes in minimal coupling theory of gauge field and gravity
• An Update on Perturbative N=8 Supergravity
• Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes
• String theory integrands and supergravity divergences
• One-Loop N = 4 Super Yang-Mills Scattering Amplitudes to All Orders in the Dimensional Regularization Parameter
• Expansion of EYM Amplitudes in Gauge Invariant Vector Space
• Supergravity limit of genus two modular graph functions in the worldline formalism
• Maximal supersymmetry and exceptional groups
• Recursive Approach to One-loop QCD Matrix Elements
• Two-loop n-point anomalous amplitudes in N=4 supergravity
• Scattering equations, supergravity integrands, and pure spinors
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• Perturbative Gravity and Twistor Space
• Light-cone gravity in dS${}_4$
• Twistors, strings and supersymmetric gauge theories
• String Theory, Unification and Quantum Gravity
• Ultra-Violet Infinities and Counterterms in Higher Dimensional Yang-Mills
• The Weyl double copy from twistor space
• Non-analytic terms of string amplitudes from partial waves
• All-loop-orders relation between Regge limits of $\mathcal{N}=4$ SYM and $\mathcal{N}=8$ supergravity four-point amplitudes
• On the non-planar beta-deformed N=4 super-Yang-Mills theory
• A technique for loop calculations in non-Abelian gauge theories - with application to five gluon amplitude
• Non--analytic terms from nested divergences in maximal supergravity
• Cosmological constant in broken maximal sugras
• Compatible Cycles and CHY Integrals
• Deformation of d=4, N> 4 Supergravities Breaks Nonlinear Local Supersymmetry
• Constraining non--BPS interactions from counterterms in three loop maximal supergravity
• TeV-scale gravity in Horava-Witten theory on a compact complex hyperbolic threefold
• Loop Amplitudes in the Coulomb Branch of $\mathcal{N}=4$ Super-Yang-Mills Theory
• Multiloop Noncommutative Open String Theory and their QFT limit
• Infrared Finite Observables in N=8 Supergravity
• On two-loop divergences of effective action in $6D$, $\mathcal{N}=(1,1)$ SYM theory
• A New Insight on Physical Phenomenology: a Review
• Spectrum, Scattering Amplitudes, and String Field Theory of 4 Dimensional Twistor String
• Symmetry Algebra of IIB Superstring Scattering
• MHV amplitudes, Wilson loops and the BDS ansatz in the superconformal N=2 QCD
• Scattering Amplitudes in Gauge Theories
• Effectively Closed Infinite-Genus Surfaces and the String Coupling
• Tree Amplitudes and Linearized SUSY Invariants in D=11 Supergravity
• Some finite terms from ladder diagrams in three and four loop maximal supergravity
• On-shell Methods for Form Factors in N=4 SYM and Their Applications
• On-Shell Perspectives on the Massless Limit of Massive Supergravity
• Scalar Gravity and the Double Copy in the Framework of General Relativity
• Two-loop corrections to $gg\to \gamma \gamma$