The Ultraviolet Properties of N=4 Supergravity at Four Loops

Abstract

We demonstrate that pure N=4 supergravity is ultraviolet divergent at four loops. The form of the divergence suggests that it is due to the rigid U(1) duality-symmetry anomaly of the theory. This is the first known example of an ultraviolet divergence in a pure ungauged supergravity theory in four dimensions. We use the duality between color and kinematics to construct the integrand of the four-loop four-point amplitude, whose ultraviolet divergence is then extracted by standard integration techniques.

5 pages, 2 figures, v2 minor corrections and added references

References in corpus (10)

• New Relations for Gauge-Theory Amplitudes
• Algorithm FIRE -- Feynman Integral REduction
• Three-Loop Superfiniteness of N=8 Supergravity
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• E7(7) constraints on counterterms in N=8 supergravity
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• 5 loops in 24/5 dimensions
• On duality symmetries of supergravity invariants
• Invariants and divergences in half-maximal supergravity theories

Cited by in corpus (116)

• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• FIRE5: a C++ implementation of Feynman Integral REduction
• Black holes and the double copy
• The classical double copy for Taub-NUT spacetime
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• Pure Gravities via Color-Kinematics Duality for Fundamental Matter
• Color-Kinematics Duality for QCD Amplitudes
• 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
• Scattering on plane waves and the double copy
• Gravitational Radiation from Color-Kinematics Duality
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Scattering Amplitudes
• Towards one-loop SYM amplitudes from the pure spinor BRST cohomology
• Gravity Amplitudes as Generalized Double Copies
• The Sub-Leading Scattering Waveform from Amplitudes
• String-inspired BCJ numerators for one-loop MHV amplitudes
• Exact solutions for the biadjoint scalar field
• New BCJ representations for one-loop amplitudes in gauge theories and gravity
• S-duality and the Double Copy
• Heterotic and bosonic string amplitudes via field theory
• Evanescent Effects Can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Double Copy from Homotopy Algebras
• Graviton-Photon Scattering
• Topology and Wilson lines: global aspects of the double copy
• Integrability of Black Hole Orbits in Maximal Supergravity
• Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• Amplitude relations in heterotic string theory and Einstein-Yang-Mills
• Gluons and gravitons at one loop from ambitwistor strings
• Double-Copy Constructions and Unitarity Cuts
• Are all supergravity theories Yang-Mills squared?
• Complete construction of magical, symmetric and homogeneous N=2 supergravities as double copies of gauge theories
• Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
• Twin Supergravities from Yang-Mills Squared
• Two-Loop Renormalization of Quantum Gravity Simplified
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• Weyl doubling
• BCJ duality and double copy in the closed string sector
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Gauged supergravities and spontaneous SUSY breaking from the double copy
• Monopoles, shockwaves and the classical double copy
• Plane wave backgrounds and colour-kinematics duality
• Biadjoint wires
• Unraveling conformal gravity amplitudes
• Construction of all N=4 conformal supergravities
• Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• One-loop Correlators and BCJ Numerators from Forward Limits
• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• Conformal Gravity from Gauge Theory
• Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Amplitudes at Infinity
• Global symmetries of Yang-Mills squared in various dimensions
• Gauge $\times$ Gauge on Spheres
• Cancelling the U(1) Anomaly in the S-matrix of N=4 Supergravity
• String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• More on the Classical Double Copy in Three Spacetime Dimensions
• Higher Derivative Supergravities in Diverse Dimensions
• N=4 conformal supergravity: the complete actions
• A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator
• Soft theorems from anomalous symmetries
• Manifesting enhanced cancellations in supergravity: integrands versus integrals
• String-motivated one-loop amplitudes in gauge theories with half-maximal supersymmetry
• Non-perturbative Double Copy in Flatland
• KLT-type relations for QCD and bicolor amplitudes from color-factor symmetry
• Absence of U(1) Anomalous Superamplitudes in $\mathcal{N}\ge 5$ Supergravities
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• Non-planarity through unitarity in ABJM
• Kinematic numerators from the worldsheet: cubic trees from labelled trees
• Gluon helicity flip in a plane wave background
• The Classical Double Copy for Half-Maximal Supergravities and T-duality
• Local BCJ numerators for ten-dimensional SYM at one loop
• The Color-Dual Fates of $F^3$, $R^3$, and $\mathcal{N}=4$ Supergravity
• Effective observables for electromagnetic duality from novel amplitude decomposition
• A double copy from twisted (co)homology at genus one
• Cancellation of Conformal and Chiral Anomalies in $N\ge 5$ supergravities
• BCJ relations from a new symmetry of gauge-theory amplitudes
• Nonlinear (Super)Symmetries and Amplitudes
• Color-Kinematics Duality for Sudakov Form Factor in Non-Supersymmetric Pure Yang-Mills Theory
• The Action with Manifest E7 Type Symmetry
• Anomalies without an action
• Color-Kinematic Duality in ABJM Theory Without Amplitude Relations
• Supersymmetry constraints on U-duality invariant deformations of $N\ge 5$ Supergravity
• FiniteFieldSolve: Exactly Solving Large Linear Systems in High-Energy Theory
• BCJ, worldsheet quantum algebra and KZ equations
• Perturbative higher-derivative terms in N=6 asymmetric orbifolds
• An Update on Perturbative N=8 Supergravity
• Next-to-MHV Yang-Mills kinematic algebra
• Two-loop n-point anomalous amplitudes in N=4 supergravity
• The Weyl double copy from twistor space
• Iwasawa nilpotency degree of non compact symmetric cosets in N-extended Supergravity
• On quantum compatibility of counterterm deformations and duality symmetries in $\mathcal{N}\ge 5$ supergravities
• Deformation of d=4, N> 4 Supergravities Breaks Nonlinear Local Supersymmetry
• Scattering amplitudes in gauge theories with and without supersymmetry
• Three-loop color-kinematics duality: A 24-dimensional solution space induced by new generalized gauge transformations
• Scalar Gravity and the Double Copy in the Framework of General Relativity
• Ambitwistor strings and amplitudes in curved backgrounds
• On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes
• Entire Four-Graviton EFT from the Duality Between Color and Kinematics
• On-Shell Perspectives on the Massless Limit of Massive Supergravity
• Color-factor symmetry and BCJ relations for QCD amplitudes