Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure

Abstract

We show that the double-copy structure of gravity forbids divergences in pure half-maximal (16 supercharge) supergravity at four and five points at one loop in D<8 and at two loops in D<6. We link the cancellations that render these supergravity amplitudes finite to corresponding ones that eliminate forbidden color factors from the divergences of pure nonsupersymmetric Yang-Mills theory. The vanishing of the two-loop four-point divergence in D=5 half-maximal supergravity is an example where a valid counterterm satisfying the known symmetries exists, yet is not present. We also give explicit forms of divergences in half-maximal supergravity at one loop in D=8 and at two loops in D=6.

32 pages, revtex, 6 figures, v3 minor corrections

References in corpus (15)

• New Relations for Gauge-Theory Amplitudes
• Algorithm FIRE -- Feynman Integral REduction
• Minimal Basis for Gauge Theory Amplitudes
• Three-Loop Superfiniteness of N=8 Supergravity
• The Momentum Kernel of Gauge and Gravity Theories
• The Kinematic Algebra From the Self-Dual Sector
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• 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
• A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
• 5 loops in 24/5 dimensions
• On duality symmetries of supergravity invariants
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory

Cited by in corpus (60)

• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• The Ultraviolet Properties of N=4 Supergravity at Four Loops
• Pure Gravities via Color-Kinematics Duality for Fundamental Matter
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• Gravitational Radiation from Color-Kinematics Duality
• Scattering on plane waves and the double copy
• Colour-Kinematics Duality for One-Loop Rational Amplitudes
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Towards one-loop SYM amplitudes from the pure spinor BRST cohomology
• Gravity Amplitudes as Generalized Double Copies
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• Equivalent D=3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories
• Evanescent Effects Can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Double Copy from Homotopy Algebras
• Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• An algebraic approach to BCJ numerators
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
• Two-Loop Renormalization of Quantum Gravity Simplified
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• BCJ duality and double copy in the closed string sector
• Post-Minkowskian Radial Action from Soft Limits and Velocity Cuts
• Hidden Simplicity of the Gravity Action
• Gauge and Gravity Amplitude Relations
• Simple encoding of higher derivative gauge and gravity counterterms
• Unraveling conformal gravity amplitudes
• Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
• Loop-Level Double-Copy for Massive Quantum Particles
• Conformal Gravity from Gauge Theory
• Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
• On powercounting in perturbative quantum gravity theories through color-kinematic duality
• Higher Derivative Supergravities in Diverse Dimensions
• Full-color three-loop three-point form factors in N=4 SYM
• A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator
• Manifesting enhanced cancellations in supergravity: integrands versus integrals
• Non-perturbative Double Copy in Flatland
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• Color-kinematics duality and dimensional reduction for graviton emission in Regge limit
• Local BCJ numerators for ten-dimensional SYM at one loop
• Gravity loop integrands from the ultraviolet
• Color-Kinematics Duality for Sudakov Form Factor in Non-Supersymmetric Pure Yang-Mills Theory
• Non-planar BCFW Grassmannian Geometries
• Color-Kinematic Duality in ABJM Theory Without Amplitude Relations
• FiniteFieldSolve: Exactly Solving Large Linear Systems in High-Energy Theory
• Poles At Infinity in On-shell Diagrams
• Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies
• Two-loop n-point anomalous amplitudes in N=4 supergravity
• Iwasawa nilpotency degree of non compact symmetric cosets in N-extended Supergravity
• Scattering amplitudes in gauge theories with and without supersymmetry
• On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes
• Three-loop color-kinematics duality: A 24-dimensional solution space induced by new generalized gauge transformations
• Ambitwistor strings and amplitudes in curved backgrounds
• Off- and on-shell harmonic superspaces for 6D SYM theories
• Smooth Splitting and Zeros from On-Shell Recursion