Classical strings and the double copy

TL;DR

This paper extends the classical double copy concept from scattering amplitudes to the dynamics of strings, specifically analyzing open and closed strings in gauge and gravity backgrounds, revealing new insights into their relationships.

Contribution

It generalizes the classical double copy to string motion, demonstrating how open string backgrounds relate to closed string backgrounds in a novel classical context.

Findings

Double copy of open strings in gauge backgrounds yields closed strings in gravity backgrounds.

No critical electric field behavior in the double copy, unlike in gauge theory.

Closed strings retain information about the gauge theory background.

Abstract

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.