Snowmass White Paper: the Double Copy and its Applications

TL;DR

The Snowmass white paper surveys the double-copy framework that relates gravity to gauge theories and, more broadly, to string theory and EFTs. It reviews tree-level (KLT/BCJ/CHY) and loop-level formulations, emphasizes the role of kinematic variables, and surveys diverse applications from classical black-hole physics to precision gravitational-wave templates, cosmology, and curved backgrounds. It also discusses generalizations, including EFTs, the KLT bootstrap, and the ongoing pursuit of a deeper kinematic algebra, as well as the unifying web of theories connected by color–kinematics duality. The work highlights open challenges—such as loop-level numerators in general theories, double-copy in curved spacetimes, and UV behavior of supergravity—while charting a roadmap for leveraging the double copy to simplify calculations and illuminate fundamental structures in QFT and string theory.

Abstract

The double copy is, in essence, a map between scattering amplitudes in a broad variety of familiar field and string theories. In addition to the mathematically rich intrinsic structure, it underlies a multitude of active research directions and has a range of interesting applications in quantum, classical and effective field theories, including broad topics such as string theory, particle physics, astrophysics, and cosmology. This Snowmass white paper provides a brief introduction to the double copy, its applications, current research and future challenges.

Figures (4)

• Figure 1: Example of the web of theories connected by the double copy. As discussed in the main text, the double copy of Yang-Mills theory (YM) with itself gives gravity; the "+" indicates that in addition to gravity one also gets the dilaton and anti-symmetric 2-form. Supersymmetry is inherited additively by the double copy; as an example $\mathcal{N}=4$ super Yang-Mills theory (sYM) with its total of 16 states --- gluons, gluinos, and scalars --- double-copies with itself to give the $16^2 = 256$ states of $\mathcal{N}=8$ supergravity (SG). Leading order 2-derivative chiral perturbation theory $\chi$PT can also act as input for the double copy and as shown in the table when it is double-copied with YM, $\mathcal{N}=4$ sYM, or itself it produces the amplitudes of a set of models relevant in various aspects of high-energy theory: Born-Infeld theory (BI) of non-linear electrodynamics, $\mathcal{N}=4$ super-Dirac Born-Infeld (sDBI), and the special Galileon (sGal) which has appeared in the contexts of modifications of gravity Nicolis:2008indeRham:2010ikdeRham:2010kj and as proposed subleading terms in brane actions deRham:2010eu. Finally, the cubic bi-adjoint scalar model (BAS) plays the role of an identity element for the double copy; we discuss this further in Section \ref{['sect:GenDC']}.
• Figure 2: Double copy constructions of string amplitudes as presented in Azevedo:2018dgo.
• Figure 3: A complete list of non-vanishing graphs contributing to four-point 2-loop $\mathcal{N}=2$ SQCD taken from ref. Johansson:2017bfl. The eight basis graphs whose kinematic weights combine to dress all graphs are (1)--(5), (13), (19) and (22).
• Figure 4: Web of theories as presented in ref. Bern:2019prr. Nodes represent the main double-copy-constructible theories, including gravitational theories (rectangular nodes), string theories (oval nodes) and non-gravitational theories (octagonal nodes). Undirected links connect theories with a common gauge-theory factor. Directed links are drawn between theories constructed by modifying both gauge-theory factors.