On powercounting in perturbative quantum gravity theories through color-kinematic duality

Abstract

The standard argument why gravity is not renormalisable relies on direct powercounting of Feynman graphs to estimate the degree of UV divergence. This analysis has in several (highly) supersymmetric examples be shown to overestimate divergences considerably. In these examples the main improvements arise from a conjectured duality between color and kinematics. In this paper we initiate the systematic study of quite general powercounting under the assumption that color-kinematic duality exists. The main technical tool is a reformulation of the duality in terms of linear maps, modulo subtleties at loop level mostly inherent to the duality. This tool may have wider applications in both gauge and gravity theories, up to resolution of the subtleties. Here it is first applied to the large Britto-Cachazo-Feng-Witten (BCFW) shift behavior of gravity integrands constructed through the duality. Assuming color-kinematic duality and reasonable technical requirements hold these shifts are shown to be independent of loop order, which would imply massive cancellations with respect to the Feynman graph expression. More speculatively, the same approach is then applied to provide estimates of the overall degree of UV divergence in quite general gravity theories, assuming the duality exists. The cancellations obtained in these estimates depends on the exact implementation of the duality at loop level, especially on graph topology. Finally, some evidence for the duality to all loop orders is provided from an analysis of BCFW shifts of gauge theory integrands through Feynman graphs.

47 pages. v2: partly rewritten for clarity, typos corrected, references updated

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Cited by in corpus (27)

• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• Color-kinematic Duality for Form Factors
• Gravitational Radiation from Color-Kinematics Duality
• Colour-Kinematics Duality for One-Loop Rational Amplitudes
• Scattering Amplitudes
• The Kinematic Algebras from the Scattering Equations
• Integrand Oxidation and One-Loop Colour-Dual Numerators in N=4 Gauge Theory
• Expansion of Einstein-Yang-Mills Amplitude
• An algebraic approach to BCJ numerators
• BCJ duality and double copy in the closed string sector
• Twistor Strings for N=8 Supergravity
• Simple encoding of higher derivative gauge and gravity counterterms
• UV considerations on scattering amplitudes in a web of theories
• Scattering equations and virtuous kinematic numerators and dual-trace functions
• Loop-Level Double-Copy for Massive Quantum Particles
• Off-shell Currents and Color-Kinematics Duality
• Classical Double Copy of Spinning Worldline Quantum Field Theory
• BCJ Identities and $d$-Dimensional Generalized Unitarity
• Kinematic Numerators and a Double-Copy Formula for N = 4 Super-Yang-Mills Residues
• Note on symmetric BCJ numerator
• Explicit BCJ numerators of nonlinear sigma model
• Gravitons, Bose-symmetry, and Bonus-scaling
• Color-Kinematic Duality in ABJM Theory Without Amplitude Relations
• BCJ, worldsheet quantum algebra and KZ equations
• BCFW Deformation and Regge Limit
• Scattering amplitudes in gauge theories with and without supersymmetry
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories