Alternative formulations of the twistor double copy

TL;DR

This paper presents two new formulations of the twistor double copy using Dolbeault cohomology, clarifying the interpretation of cohomology representatives and enhancing the mathematical framework for relating solutions in gauge and gravity theories.

Contribution

It introduces alternative Dolbeault cohomology formulations of the twistor double copy, improving understanding and potential applications of twistor methods in the double copy correspondence.

Findings

Rewritten Cech approach in Dolbeault language

Identification of special cohomology representatives in Euclidean signature

Potential for further applications of twistor methods in double copy

Abstract

The classical double copy relating exact solutions of biadjoint scalar, gauge and gravity theories continues to receive widespread attention. Recently, a derivation of the exact classical double copy was presented, using ideas from twistor theory, in which spacetime fields are mapped to Cech cohomology classes in twistor space. A puzzle remains, however, in how to interpret the twistor double copy, in that it relies on somehow picking special representatives of each cohomology class. In this paper, we provide two alternative formulations of the twistor double copy using the more widely-used language of Dolbeault cohomology. The first amounts to a rewriting of the Cech approach, whereas the second uses known techniques for discussing spacetime fields in Euclidean signature. The latter approach indeed allows us to identify special cohomology representatives, suggesting that further application of twistor methods in exploring the remit of the double copy may be fruitful.