Gauge $\times$ Gauge on Spheres

Abstract

We introduce a convolution on a 2-sphere and use it to show that the linearised Becchi-Rouet-Stora-Tyutin transformations and gauge fixing conditions of Einstein-Hilbert gravity coupled to a two-form and a scalar field, follow from the product of two Yang-Mills theories. This provides an example of the convolutive product of gauge theories on a non-trivial background. By introducing a time direction the product is shown to extend to the $D=1+2$ Einstein-static universe.

arXiv comment24 pages

References in corpus (101)

• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Amplitudes, Observables, and Classical Scattering
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• Gravity as the Square of Gauge Theory
• Minimal Basis for Gauge Theory Amplitudes
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Black holes and the double copy
• Antibracket, Antifields and Gauge-Theory Quantization
• Ambitwistor strings and the scattering equations
• The Ultraviolet Behavior of N=8 Supergravity at Four Loops
• The Momentum Kernel of Gauge and Gravity Theories
• The Kinematic Algebra From the Self-Dual Sector
• The classical double copy for Taub-NUT spacetime
• Observables and amplitudes for spinning particles and black holes
• Explicit BCJ Numerators from Pure Spinors
• Kerr Black Holes as Elementary Particles
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• Ambitwistor strings and the scattering equations at one loop
• Perturbative spacetimes from Yang-Mills theory
• Loop Integrands for Scattering Amplitudes from the Riemann Sphere
• The double copy: Bremsstrahlung and accelerating black holes
• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• 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
• 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
• Algebras for Amplitudes
• Double copy for massive quantum particles with spin
• Classical gluon and graviton radiation from the bi-adjoint scalar double copy
• Yang-Mills origin of gravitational symmetries
• Scattering on plane waves and the double copy
• Gravitational Radiation from Color-Kinematics Duality
• Colour-Kinematics Duality for One-Loop Rational Amplitudes
• Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Type D Spacetimes and the Weyl Double Copy
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• Symmetry and Action for Flavor-Kinematics Duality
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• BCJ duality and the double copy in the soft limit
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• Perturbative Gravity from QCD Amplitudes
• Proof of the Formula of Cachazo, He and Yuan for Yang-Mills Tree Amplitudes in Arbitrary Dimension
• New Relations for Three-Dimensional Supersymmetric Scattering Amplitudes
• Gravity as Gauge Theory Squared: A Ghost Story
• Double copy structure of CFT correlators
• Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy
• The Kinematic Algebras from the Scattering Equations
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• Color/kinematics duality for general abelian orbifolds of N=4 super Yang-Mills theory
• Effective action of dilaton gravity as the classical double copy of Yang-Mills theory
• Static Spherically Symmetric Kerr-Schild Metrics and Implications for the Classical Double Copy
• String-inspired BCJ numerators for one-loop MHV amplitudes
• Exact solutions for the biadjoint scalar field
• Semi-abelian Z-theory: NLSM+phi^3 from the open string
• Equivalent D=3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories
• S-duality and the Double Copy
• On the U(1) duality anomaly and the S-matrix of N=4 supergravity
• Heterotic and bosonic string amplitudes via field theory
• Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality
• Evanescent Effects Can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• A double copy for $\mathcal{N}=2$ supergravity: a linearised tale told on-shell
• A magic pyramid of supergravities
• Manifesting Color-Kinematics Duality in the Scattering Equation Formalism
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO
• Are all supergravity theories Yang-Mills squared?
• Complete construction of magical, symmetric and homogeneous N=2 supergravities as double copies of gauge theories
• Twofold Symmetries of the Pure Gravity Action
• Twin Supergravities from Yang-Mills Squared
• On factorizations in perturbative quantum gravity
• CHY representations for gauge theory and gravity amplitudes with up to three massive particles
• BCJ duality and double copy in the closed string sector
• Constraints and Generalized Gauge Transformations on Tree-Level Gluon and Graviton Amplitudes
• Kerr-Schild Double Copy and Complex Worldlines
• Hidden Simplicity of the Gravity Action
• Gauged supergravities and spontaneous SUSY breaking from the double copy
• A magic square from Yang-Mills squared
• Biadjoint wires
• Superconformal symmetry and maximal supergravity in various dimensions
• Gravity as the square of Yang-Mills?
• $D=6$, $\mathcal{N}=(2,0)$ and $\mathcal{N}=(4,0)$ theories
• The Double Copy of Massive Scalar-QCD
• Ambitwistor formulations of $R^2$ gravity and $(DF{)}^2$ gauge theories
• Colour-Kinematics duality and the Drinfeld double of the Lie algebra of diffeomorphisms
• Virtual Color-Kinematics Duality: 6-pt 1-Loop MHV Amplitudes
• Global symmetries of Yang-Mills squared in various dimensions
• The Complete KLT-Map Between Gravity and Gauge Theories
• On General BCJ Relation at One-loop Level in Yang-Mills Theory
• KLT-type relations for QCD and bicolor amplitudes from color-factor symmetry
• Chiral Squaring
• Spin-four N=7 W-Supergravity: S-fold and Double Copy Construction
• Twin conformal field theories

Cited by in corpus (21)

• Classical Solutions and their Double Copy in Split Signature
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• The convolutional double copy: a case study with a point
• Classical Yang-Mills observables from amplitudes
• A double copy for asymptotic symmetries in the self-dual sector
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• Weyl doubling
• Classical and quantum double copy of back-reaction
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Massive Gravity from Double Copy
• Asymptotic Weyl Double Copy
• Alternative formulations of the twistor double copy
• On the Lagrangian formulation of the double copy to cubic order
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• BRST Symmetry and the Convolutional Double Copy
• Next-to-MHV Yang-Mills kinematic algebra
• The Weyl double copy from twistor space
• NS-NS Spacetimes from Amplitudes
• Ersatz gravity and black-hole thermodynamics from Manin gauge theory with noncompact gauge group