Phys. Rev. D, 111, L081902 (2025)

Five dimensional Weyl double copy

Weicheng Zhao¹, Pu-Jian Mao¹ and Jun-Bao Wu^1,2

1 Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, 135 Yaguan Road, Tianjin 300350, China.

2 Peng Huanwu Center for Fundamental Theory, Hefei, Anhui 230026, China

* zhaoweichengok@dgquanwei.com, pjmao@dgquanwei.com, junbao.wu@dgquanwei.com

Abstract

The Weyl double copy (WDC) relation connects the Weyl tensor of the gravity theory and the field strength tensor of the Maxwell theory, which provides a concrete realization of the classical double copy. Although intensively investigated, the WDC is only limited in four-dimensional spacetime. In this Letter, we generalize the WDC relation to five-dimensional spacetime, which offers the first example of the WDC in higher dimensions. We show that a special class of five-dimensional type N vacuum solutions admits a special class of degenerate Maxwell field that squares to give the Weyl tensor. The five-dimensional WDC relation defines a scalar field that satisfies the source-free Klein-Gordon equation on the curved background. We further verify that for five-dimensional pp-wave solution and Kundt solutions, the Maxwell fields and the scalar fields also satisfy the Maxwell's equations and the wave equation on five-dimensional Minkowski spacetime.