Double copy of spontaneously broken Abelian gauge theory

TL;DR

This paper demonstrates how solutions in spontaneously broken Abelian gauge theories can be expressed as double copies, leading to new insights into black hole-like objects and quantum states with string-like characteristics.

Contribution

It provides a direct realization of the double copy concept from solutions of Einstein's equations, specifically for spontaneously broken scalar electrodynamics.

Findings

Derived a general energy momentum tensor for electric fields.

Found a double copy relation for a screened Reissner-Nordström metric.

Identified string-like behavior in highly excited quantum states.

Abstract

Similarity in the structure of scattering amplitudes in Yang-Mills theories and General Relativity led to the idea that graviton could be described as the double copy of a vector gauge field. In this letter we discuss a realization of this idea emerging directly from solutions of equations of General Relativity. A general form of the energy momentum tensor for the electric field is derived that leads to the metric tensor in terms of the double copy of a corresponding gauge potential. We than use this general property to find the double copy of spontaneously broken scalar electrodynamics. The result is a screened Reissner-Nordstr\"om-like metric. When the horizon radius and the Compton wavelength of the massive photon become comparable the black hole becomes a quantum object. An exact solution of the horizon wave equation is found and the corresponding energy spectrum is described. It turns out that highly excited states show a characteristic string-like behavior.