Equations of Motion Solved by the Cremmer-Scherk Configuration on Even-Dimensional Spheres

TL;DR

This paper demonstrates that the Cremmer-Scherk configuration provides classical solutions to a broad class of non-Abelian gauge theories on even-dimensional spheres, including complex multi-trace Lagrangians, leveraging generalized self-duality.

Contribution

It shows that the Cremmer-Scherk configuration solves equations of motion for arbitrary C^1 functions of specific gauge-invariant quantities, extending known solutions to more general theories.

Findings

Cremmer-Scherk configuration solves equations of motion for a wide class of actions.

Includes multi-trace Lagrangians in the solution class.

Potential for classifying actions based on stability against this configuration.

Abstract

Equations of motion of low-energy effective theories of quantum electrodynamics include infinitely many interaction terms, which make them difficult to solve. The self-duality property has facilitated research on the solutions to these equations. In this paper, equations of motion of systems of non-Abelian gauge fields on even-dimensional spheres are considered. It is demonstrated that the Cremmer-Scherk configuration, which satisfies certain generalized self-duality equations, becomes the classical solution for the class of systems that are given by arbitrary functions of class C^1 of 2m+1 quantities. For instance, Lagrangians consisting of multi-trace terms are included in this class. This result is likely to generate several new and interesting directions of research, including the classification of actions with respect to the stability condition against the Cremmer-Scherk configuration.