Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes

Abstract

We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N=4 super-Yang-Mills theory, including the nonplanar contributions. The duality completely determines the amplitude's integrand in terms of just two planar graphs. The existence of a manifestly dual gauge-theory amplitude trivializes the construction of the corresponding N=8 supergravity integrand, whose graph numerators are double copies (squares) of the N=4 super-Yang-Mills numerators. The success of this procedure provides further nontrivial evidence that the duality and double-copy properties hold at loop level. The new form of the four-loop four-point supergravity amplitude makes manifest the same ultraviolet power counting as the corresponding N=4 super-Yang-Mills amplitude. We determine the amplitude's ultraviolet pole in the critical dimension of D=11/2, the same dimension as for N=4 super-Yang-Mills theory. Strikingly, exactly the same combination of vacuum integrals (after simplification) describes the ultraviolet divergence of N=8 supergravity as the subleading-in-1/N_c^2 single-trace divergence in N=4 super-Yang-Mills theory.

v2: PRD published version, fixed glitch in ancillary file. v1: 61 pages, 22 figures

References in corpus (40)

• New Relations for Gauge-Theory Amplitudes
• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Minimal Basis for Gauge Theory Amplitudes
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Three-Loop Superfiniteness of N=8 Supergravity
• The Momentum Kernel of Gauge and Gravity Theories
• The Kinematic Algebra From the Self-Dual Sector
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• Amplitudes and Spinor-Helicity in Six Dimensions
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• Is N = 8 Supergravity Ultraviolet Finite?
• E7(7) constraints on counterterms in N=8 supergravity
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Ultraviolet properties of Maximal Supergravity
• Master Integrals for Four-Loop Massless Propagators up to Transcendentality Weight Twelve
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• Exacting N=4 Superconformal Symmetry
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
• 5 loops in 24/5 dimensions
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• 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
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• Iterative Structure Within The Five-Particle Two-Loop Amplitude
• Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight
• Calculating multiloop integrals using dimensional recurrence relation and D-analyticity
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• N=8 Counterterms and E7(7) Current Conservation
• The Ultraviolet Finiteness of N=8 Supergravity
• Linear relations between N >= 4 supergravity and subleading-color SYM amplitudes
• The D^{2k} R^4 Invariants of N=8 Supergravity

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• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
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