# Spinning particles, axion radiation, and the classical double copy

## Abstract

We extend the perturbative double copy between radiating classical sources in gauge theory and gravity to the case of spinning particles. We construct, to linear order in spins, perturbative radiating solutions to the classical Yang-Mills equations sourced by a set of interacting color charges with chromomagnetic dipole spin couplings. Using a color-to-kinematics replacement rule proposed earlier by one of the authors, these solutions map onto radiation in a theory of interacting particles coupled to massless fields that include the graviton, a scalar (dilaton) Φ and the Kalb-Ramond axion field B_{μν}. Consistency of the double copy imposes constraints on the parameters of the theory on both the gauge and gravity sides of the correspondence. In particular, the color charges carry a chromomagnetic interaction which, in d = 4, corresponds to a gyromagnetic ratio equal to Dirac’s value g = 2. The color-to-kinematics map implies that on the gravity side, the bulk theory of the fields (Φ; g_{μν}; B_{μν}) has interactions which match those of d-dimensional “string gravity,” as is the case both in the BCJ double copy of pure gauge theory scattering amplitudes and the KLT relations between the tree-level S-matrix elements of open and closed string theory.

- Authors:

- Publication Date:

- Research Org.:
- Yale Univ., New Haven, CT (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1439386

- Alternate Identifier(s):
- OSTI ID: 1503840

- Grant/Contract Number:
- SC0017660

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 10; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Goldberger, Walter D., Li, Jingping, and Prabhu, Siddharth G. Spinning particles, axion radiation, and the classical double copy. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.97.105018.
```

```
Goldberger, Walter D., Li, Jingping, & Prabhu, Siddharth G. Spinning particles, axion radiation, and the classical double copy. United States. doi:10.1103/PhysRevD.97.105018.
```

```
Goldberger, Walter D., Li, Jingping, and Prabhu, Siddharth G. Tue .
"Spinning particles, axion radiation, and the classical double copy". United States. doi:10.1103/PhysRevD.97.105018.
```

```
@article{osti_1439386,
```

title = {Spinning particles, axion radiation, and the classical double copy},

author = {Goldberger, Walter D. and Li, Jingping and Prabhu, Siddharth G.},

abstractNote = {We extend the perturbative double copy between radiating classical sources in gauge theory and gravity to the case of spinning particles. We construct, to linear order in spins, perturbative radiating solutions to the classical Yang-Mills equations sourced by a set of interacting color charges with chromomagnetic dipole spin couplings. Using a color-to-kinematics replacement rule proposed earlier by one of the authors, these solutions map onto radiation in a theory of interacting particles coupled to massless fields that include the graviton, a scalar (dilaton) Φ and the Kalb-Ramond axion field Bμν. Consistency of the double copy imposes constraints on the parameters of the theory on both the gauge and gravity sides of the correspondence. In particular, the color charges carry a chromomagnetic interaction which, in d = 4, corresponds to a gyromagnetic ratio equal to Dirac’s value g = 2. The color-to-kinematics map implies that on the gravity side, the bulk theory of the fields (Φ; gμν; Bμν) has interactions which match those of d-dimensional “string gravity,” as is the case both in the BCJ double copy of pure gauge theory scattering amplitudes and the KLT relations between the tree-level S-matrix elements of open and closed string theory.},

doi = {10.1103/PhysRevD.97.105018},

journal = {Physical Review D},

number = 10,

volume = 97,

place = {United States},

year = {2018},

month = {5}

}

DOI: 10.1103/PhysRevD.97.105018

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