Is covariant star product unique?

Vassilevich, D. V.

doi:10.22323/1.127.0006

Cited by 1 publication

(1 citation statement)

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“…those of refs. [136,137], which may to lead to different quantum field theories). Finally, our hope is that the results of our study may stimulate the construction of yet more double copy examples, which may possibly in turn enhance our understanding of conventional Yang-Mills and gravity beyond the self-dual sector.…”

Section: Discussionmentioning

confidence: 99%

New heavenly double copies

Chacón

García‐Compeán

Luna³

et al. 2021

J. High Energ. Phys.

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The double copy relates scattering amplitudes and classical solutions in Yang-Mills theory, gravity, and related field theories. Previous work has shown that this has an explicit realisation in self-dual YM theory, where the equation of motion can be written in a form that maps directly to Plebański’s heavenly equation for self-dual gravity. The self-dual YM equation involves an area-preserving diffeomorphism algebra, two copies of which appear in the heavenly equation. In this paper, we show that this construction is a special case of a wider family of heavenly-type examples, by (i) performing Moyal deformations, and (ii) replacing the area-preserving diffeomorphisms with a less restricted algebra. As a result, we obtain a double-copy interpretation for hyper-Hermitian manifolds, extending the previously known hyper-Kähler case. We also introduce a double-Moyal deformation of the heavenly equation. The examples where the construction of Lax pairs is possible are manifestly consistent with Ward’s conjecture, and suggest that the classical integrability of the gravity-type theory may be guaranteed in general by the integrability of at least one of two gauge-theory-type single copies.

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Section: Discussionmentioning

confidence: 99%