Non-perturbative aspects of the self-dual double copy

Abstract

The double copy is by now a firmly-established correspondence between amplitudes and classical solutions in biadjoint scalar, gauge and gravity theories. To date, no strongly coupled examples of the double copy in four dimensions have been found, and previous attempts based on exact non-linear solutions of biadjoint theory in Lorentzian signature have failed. In this paper, we instead look for biadjoint solutions in Euclidean signature, which may be relatable to Yang-Mills or gravitational instantons. We show that spherically symmetric power-like Euclidean solutions do not exist in precisely four spacetime dimensions. The explanation for why this is the case turns out to involve the Eguchi-Hanson instanton, whose single copy structure is found to be more complicated (and interesting) than previously thought. We provide a more general prescription for double-copying instantons, and explain how our results provide a higher-dimensional complement to a recently presented non-perturbative double copy of exact solutions in two spacetime dimensions. In doing so, we demonstrate how the replacement of colour by kinematic Lie algebras operates at the level of exact classical solutions.

29 pages, 5 figures

References in corpus (36)

• New Relations for Gauge-Theory Amplitudes
• Black holes and the double copy
• The Kinematic Algebra From the Self-Dual Sector
• Effective Field Theories from Soft Limits
• The Kerr-Schild double copy in curved spacetime
• Yang-Mills origin of gravitational symmetries
• A Twistorial Foundation for the Classical Double Copy
• The Weyl Double Copy for Gravitational Waves
• Double Copy from Homotopy Algebras
• Classical Solutions and their Double Copy in Split Signature
• Topology and Wilson lines: global aspects of the double copy
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• Covariant Color-Kinematics Duality
• The convolutional double copy: a case study with a point
• Extended solutions for the biadjoint scalar field
• A double copy for asymptotic symmetries in the self-dual sector
• Twofold Symmetries of the Pure Gravity Action
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• Weyl doubling
• The Newman-Penrose Map and the Classical Double Copy
• Classical double copy at null infinity
• Monopoles, shockwaves and the classical double copy
• Strings, extended objects, and the classical double copy
• New heavenly double copies
• Geometry-Kinematics Duality
• Asymptotic Weyl Double Copy
• Kerr-Schild Double Copy of the Coulomb Solution in Three Dimensions
• Unfolded Description of $Ad{S}_4$ Kerr Black Hole
• Alternative formulations of the twistor double copy
• Twistor Space Origins of the Newman-Penrose Map
• The double copy of the multipole expansion
• Yang-Mills Instantons from Gravitational Instantons
• The single copy of the gravitational holonomy
• Non-perturbative Double Copy in Flatland
• Double copy for Lagrangians at trilinear order
• Reconstructing Classical Spacetimes from the S-Matrix in Twistor Space

Cited by in corpus (6)

• Amplitudes, Hopf algebras and the colour-kinematics duality
• Isometries and the double copy
• 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
• A spinorial double copy for $\mathcal{N}=0$ supergravity
• Hawking radiation from the double copy