[Paper Review] Analogue of black string in the Yang--Mills gauge theory

Yuri N. Obukhov|ArXiv.org|Aug 1, 1996

Black Holes and Theoretical Physics1 references4 citations

TL;DR

This paper constructs exact analytical solutions for cylindrically symmetric Yang--Mills gauge and isoscalar fields within an effective gravity framework, revealing an infinite family of configurations with a finite radial singularity. These solutions model 'thick string'-like objects that confine gauge-charged particles both classically and quantum mechanically, serving as direct analogues to black strings in gravity, with confinement arising from a simple pole in the radial field profile.

ABSTRACT

The classical Yang--Mills equations are analyzed within the geometrical framework of an effective gravity theory. Exact analytical solutions are derived for the cylindrically symmetric configurations of the coupled gauge and isoscalar fields. It turns out that there is an infinite family of solutions parametrized by two real parameters, one of which determines the asymptotic behavior of fields near the symmetry axis and in infinity, while the second locates the singularity. These configurations have a simple pole at a finite value of the radial coordinate, and physically they represent ``thick string''-like objects which possess the confinement properties. It is demonstrated that the particles with gauge charge cannot move classically and quantum mechanically out of the interior region. Such an objects are thus direct analogues of the ``black string'' gravitational configurations reported recently in the literature.

Motivation & Objective

• To explore classical solutions of the Yang--Mills equations in a geometric effective gravity framework.
• To identify cylindrically symmetric configurations of coupled gauge and isoscalar fields that exhibit confinement-like behavior.
• To determine whether such configurations can trap gauge-charged particles, mimicking the behavior of black strings in gravity.
• To establish the existence of an infinite family of exact solutions parametrized by two real parameters.
• To analyze the classical and quantum mechanical motion of particles with gauge charge within these configurations.

Proposed method

• The study employs a geometric formulation of an effective gravity theory to analyze the classical Yang--Mills equations.
• It assumes cylindrical symmetry and derives exact analytical solutions for coupled gauge and isoscalar fields.
• The solutions are parametrized by two real parameters: one governing asymptotic field behavior at infinity and the symmetry axis, the other locating the radial singularity.
• The field configuration features a simple pole at a finite radial coordinate, indicating a singular structure.
• The dynamics of gauge-charged particles are analyzed classically and quantum mechanically to assess confinement.
• The analysis demonstrates that particles cannot escape the interior region due to the field singularity and potential barrier.

Experimental results

Research questions

• RQ1 Can exact analytical solutions be derived for cylindrically symmetric Yang--Mills and isoscalar fields in an effective gravity framework?
• RQ2 Do these solutions exhibit properties analogous to black strings in general relativity, particularly confinement?
• RQ3 What is the role of the two real parameters in characterizing the family of solutions and their physical behavior?
• RQ4 Can gauge-charged particles classically or quantum mechanically escape the region near the singularity?
• RQ5 How does the radial field singularity influence the dynamics and confinement of charged particles?

Key findings

• An infinite family of exact analytical solutions exists, parameterized by two real numbers: one controlling asymptotic field behavior, the other locating the radial singularity.
• The solutions exhibit a simple pole at a finite radial coordinate, indicating a singular structure that confines gauge-charged particles.
• Particles with gauge charge cannot move out of the interior region in either classical or quantum mechanical treatments, due to the field configuration.
• The configurations behave as 'thick strings' with confinement properties, analogous to black strings in gravitational theories.
• The singularity and field profile create a potential barrier that prevents escape of gauge-charged particles, ensuring confinement.