Time-dependent solutions of biadjoint scalar field theories

TL;DR

This paper introduces new exact, time-dependent solutions in biadjoint scalar field theories, including massive and quartic extensions, with some solutions being bounded, advancing understanding of non-perturbative gauge-gravity relations.

Contribution

The authors present novel analytical solutions for biadjoint scalar theories, including generalizations with mass, quartic terms, and background fields, expanding the solution space and connecting to soliton studies.

Findings

Existence of exact time-dependent solutions

Introduction of mass and quartic terms yields new solutions

Discovery of bounded solutions contrasting previous examples

Abstract

Biadjoint scalar field theories appear in the study of scattering amplitudes and classical solutions in gauge, gravity and related theories. In this paper, we present new exact solutions of biadjoint scalar field theory, showing that time-dependent solutions are possible and analytically tractable. We generalise the theory to include mass and / or quartic terms, and also a coupling to a constant background field. This allows for more exact solutions, which make contact with previous soliton literature. We also find bounded solutions, in contrast to all known previous examples. Our results may be useful for the study of non-perturbative aspects of the double copy between gauge theories and gravity. We also speculate as to their possible practical applications.