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A double copy for asymptotic symmetries in the self-dual sector

Miguel Campiglia, Silvia Nagy

TL;DR

The work presents a concrete double copy dictionary for symmetries of the self-dual sectors of Yang-Mills and gravity in the light-cone gauge, uncovering two infinite families tied to residual gravitational diffeomorphisms. It shows nonperturbative bulk double copy rules and a perturbative-to-nonlocal mapping in the YM sector that produce nontrivial gravitational symmetries, with a clear null-infinity realization. At null infinity, holomorphic YM large gauge transformations double copy to holomorphic supertranslations, while certain non-gauge YM transformations double copy to superrotations, revealing a rich structure linking bulk and boundary symmetries. The results extend the color-kinematics duality to an entire tower of asymptotic symmetries, with a symmetry-raising map commuting with the DC, suggesting a path toward broader applicability beyond self-duality and potentially informing celestial amplitude and memory-effect frameworks.

Abstract

We give a double copy construction for the symmetries of the self-dual sectors of Yang-Mills (YM) and gravity, in the light-cone formulation. We find an infinite set of double copy constructible symmetries. We focus on two families which correspond to the residual diffeomorphisms on the gravitational side. For the first one, we find novel non-perturbative double copy rules in the bulk. The second family has a more striking structure, as a non-perturbative gravitational symmetry is obtained from a perturbatively defined symmetry on the YM side. At null infinity, we find the YM origin of the subset of extended Bondi-Metzner-Sachs (BMS) symmetries that preserve the self-duality condition. In particular, holomorphic large gauge YM symmetries are double copied to holomorphic supertranslations. We also identify the single copy of superrotations with certain non-gauge YM transformations that to our knowledge have not been previously presented in the literature.

A double copy for asymptotic symmetries in the self-dual sector

TL;DR

The work presents a concrete double copy dictionary for symmetries of the self-dual sectors of Yang-Mills and gravity in the light-cone gauge, uncovering two infinite families tied to residual gravitational diffeomorphisms. It shows nonperturbative bulk double copy rules and a perturbative-to-nonlocal mapping in the YM sector that produce nontrivial gravitational symmetries, with a clear null-infinity realization. At null infinity, holomorphic YM large gauge transformations double copy to holomorphic supertranslations, while certain non-gauge YM transformations double copy to superrotations, revealing a rich structure linking bulk and boundary symmetries. The results extend the color-kinematics duality to an entire tower of asymptotic symmetries, with a symmetry-raising map commuting with the DC, suggesting a path toward broader applicability beyond self-duality and potentially informing celestial amplitude and memory-effect frameworks.

Abstract

We give a double copy construction for the symmetries of the self-dual sectors of Yang-Mills (YM) and gravity, in the light-cone formulation. We find an infinite set of double copy constructible symmetries. We focus on two families which correspond to the residual diffeomorphisms on the gravitational side. For the first one, we find novel non-perturbative double copy rules in the bulk. The second family has a more striking structure, as a non-perturbative gravitational symmetry is obtained from a perturbatively defined symmetry on the YM side. At null infinity, we find the YM origin of the subset of extended Bondi-Metzner-Sachs (BMS) symmetries that preserve the self-duality condition. In particular, holomorphic large gauge YM symmetries are double copied to holomorphic supertranslations. We also identify the single copy of superrotations with certain non-gauge YM transformations that to our knowledge have not been previously presented in the literature.

Paper Structure

This paper contains 42 sections, 223 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Self-dual fields
  3. Symmetries of the self-dual field equations
  4. Residual gauge symmetries
  5. YM field
  6. Metric field
  7. First family of symmetries
  8. Second family of symmetries
  9. Perturbative approach to symmetries
  10. YM field
  11. Metric field
  12. First family of symmetries
  13. Second family of symmetries
  14. Color to kinematics map for symmetries
  15. First family of symmetries
  16. ...and 27 more sections

Figures (1)

  • Figure 1: Summary of the asymptotic symmetries and their various relations. LGT stands for non-abelian large gauge transformations, ST and SR for supertranslations and superrotations. Horizontal lines represent the DC relations. Vertical lines represent the symmetry raising map between the first and second family of symmetries. Diagonal arrows represent an increase in the power of $r$ of symmetry parameters, see main text for details.