Worldline Approach to the Double Copy

• Applicant: Dr. Roberto Bonezzi, Ph.D.
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 524744955

The double copy is a powerful framework that allows to compute gravitational scattering amplitudes by using much simpler gauge theory amplitudes as building blocks. Since its discovery in string theory in the mid eighties, the double copy program has grown considerably over the years, and at present it is often the best approach to deal with otherwise intractable problems in gravity. Despite its many successes, a first-principles understanding of the double copy is still lacking. Most notably, this is reflected in the absence of a clear prescription for the double copy beyond the realm of scattering amplitudes. It is the aim of this research proposal to lay the ground for an off-shell and gauge invariant construction of the double copy, thereby going beyond the amplitude level. I plan to do so by combining worldline techniques and an algebraic approach to perturbative field theory. The worldline formalism shares many similarities with string theory, including the double copy form of the gravitational spectrum, which makes it a promising approach for tackling the problem. In conjunction with this, I will rely on algebraic methods which treat both Yang-Mills and gravity as homotopy Lie algebras. These are generalizations of Lie algebras, including higher brackets, which can be associated to any perturbative field theory. This method is particularly well suited for an off-shell and gauge invariant extension of the double copy, in that the consistency of all interactions and nonlinear gauge symmetries is encoded at once in a set of generalized Jacobi identities. The effectiveness of this approach has been corroborated in a recent work by me and my collaborators, which provides an off-shell and gauge invariant double copy of Yang-Mills theory at cubic order. More specifically, the proposal is divided into three main projects. The aim of the first part is to uplift the duality between color and kinematics, a property of Yang-Mills amplitudes which is central to the double copy, to an off-shell algebra. There is indeed some preliminary evidence for a higher algebraic structure to exist, which seems to reproduce the so-called kinematic Jacobi identities. This algebraic structure will be central for the second part of the proposal, whose goal is to establish an off-shell double copy of Yang-Mills beyond cubic and possibly to all orders. The consistency of this construction should be kept under control by the underlying algebraic relations of the single copies. Extensions of this project will be about projection to pure Einstein gravity and including supersymmetry. Finally, I intend to explore potential applications of an off-shell double copy prescription. In this regard, the main focus will be on the double copy structure of classical solutions, which could be studied in a systematic way, at least for perturbative regimes.

• DFG Programme: Research Grants