Classical strings and the double copy

The double copy is by now a well-established relationship between scattering amplitudes and classical solutions in gauge and gravity (field) theories, and is itself inspired by amplitude relations in string theory. In this paper, we generalise the classical double copy to the motion of strings, taking as a case study the motion of an open string in a background abelian gauge field. We argue that the double copy of this situation is a closed string moving in a spacetime background arising as the double copy of the gauge theory background. The gauge theory background we consider is that of a constant electric field, which has a critical value beyond which the open string motion is pathological. We find no counterpart of this behaviour in the double copy, and interpret this result. We then examine how the closed string nevertheless still knows about the single copy gauge theory. Our results pave the way for more systematic study of the double copy in a classical string context, thus going beyond the KLT relations for amplitudes in flat space.

💡 Research Summary

The paper extends the well‑established classical double copy—originally a correspondence between gauge‑theory and gravity solutions—to the dynamics of strings. Using the Kerr‑Schild formalism, the authors first review how a metric of the form (g_{\mu\nu}= \eta_{\mu\nu}+ \kappa ,\phi,k_\mu k_\nu) linearises the Einstein equations, and how the associated gauge field (A_\mu = \phi,k_\mu) automatically satisfies the Maxwell equations. They then specialise to a constant electric field background. By choosing a scalar profile (\phi(x)=f,x) and a null vector (k_\mu) aligned with the light‑cone direction, the gauge potential becomes (A = \sqrt{2},f,x,du), which yields a uniform electric field (E_x = f) in the (x)‑direction.

The double copy of this gauge configuration produces the metric
\