Exact Schwarzschild-Like Solution for SU(N) Gauge Theory

TL;DR

This paper derives an exact, spherically symmetric solution for SU(N+1) gauge theory coupled to a scalar field, resembling a Schwarzschild black hole, and suggests it could explain confinement in non-Abelian gauge theories.

Contribution

It extends an earlier SU(2) solution to SU(N+1), providing an exact analytical solution using the Bogomolny formalism, and explores its implications for confinement.

Findings

Solution is similar to Schwarzschild metric with divergence at radius r_0

Proposes a confinement mechanism where particles are trapped inside r_0

Calculates the energy of the gauge and scalar field configuration

Abstract

In this paper we extend our previously discovered exact solution for an SU(2) gauge theory coupled to a massless, non-interacting scalar field, to the general group SU(N+1). Using the first-order formalism of Bogomolny, an exact, spherically symmetric solution for the gauge and scalar fields is found. This solution is similiar to the Schwarzschild solution of general relativity, in that the gauge and scalar fields become infinite at a radius, $r_0 = K$, from the origin. It is speculated that this may be the confinement mechanism that has long been sought for in non-Abelian gauge theories, since any particle which carries the SU(N+1) charge would become permanently trapped once it entered the region $r < r_0$. The energy of the field configuration of this solution is calculated.