Double Copy from Homotopy Algebras

Leron Borsten,Branislav Jurčo,Martin Wolf,Christian Saemann,Tommaso Macrelli,Hyungrok Kim

doi:10.1002/prop.202100075

Leron Borsten, Branislav Jurčo + Show 4 more

Open Access

https://doi.org/10.1002/prop.202100075

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Abstract

AbstractWe show that the BRST Lagrangian double copy construction of supergravity as the ‘square’ of Yang–Mills theory finds a natural interpretation in terms of homotopy algebras. We significantly expand on our previous work arguing the validity of the double copy at the loop level, and we give a detailed derivation of the double‐copied Lagrangian and BRST operator. Our constructions are very general and can be applied to a vast set of examples.

Highlights

Introduction and resultsRecent years have witnessed a resurgence of the idea that gravity can, in some sense, be viewed as the product of two gauge theories,‘gravity “ gauge b gauge’ . (1.1)This notion goes back at least to the 1960’s [1, 2] and was realised concretely at the level of tree-level scattering amplitudes via the Kawai–Lewellen–Tye (KLT) relations of string theory [3]: closed string tree amplitudes can be written as sums over products of open string tree amplitudes
The field theory limit of the KLT relations implies a relationship between tree-level Yang–Mills amplitudes and those of N “ 0 supergravity, the universal massless sector of closed string theories consisting of Einstein–Hilbert gravity coupled to a Kalb–Ramond two-form and dilaton. This paradigm was dramatically advanced with the advent of the Bern–Carrasco– Johansson (BCJ) colour–kinematics duality and the double copy prescription [4–6]
We provide an explicit account of the BRST–Lagrangian double copy [9] and its articulation in terms of homotopy algebras

Summary

Introduction

Introduction and resultsRecent years have witnessed a resurgence of the idea that gravity can, in some sense, be viewed as the product of two gauge theories,‘gravity “ gauge b gauge’ . (1.1)This notion goes back at least to the 1960’s [1, 2] and was realised concretely at the level of tree-level scattering amplitudes via the Kawai–Lewellen–Tye (KLT) relations of string theory [3]: closed string tree amplitudes can be written as sums over products of open string tree amplitudes. The field theory limit of the KLT relations implies a relationship between tree-level Yang–Mills amplitudes and those of N “ 0 supergravity, the universal massless sector of closed string theories consisting of Einstein–Hilbert gravity coupled to a Kalb–Ramond two-form and dilaton. This paradigm was dramatically advanced with the advent of the Bern–Carrasco– Johansson (BCJ) colour–kinematics duality and the double copy prescription [4–6]. It was conjectured [4] that gluon amplitudes can be recast so as to manifest a duality between their colour and kinematical data. Given a gluon amplitude in colour– kinematics-dual form, it can be ‘double-copied’ to yield a bona fide amplitude of N “ 0 supergravity

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Conclusion