On Emergent Particles and Stable Neutral Plasma Balls in SU(2) Yang-Mills Thermodynamics

Ralf Hofmann,Thierry Grandou

doi:10.3390/universe8020117

Ralf Hofmann, Thierry Grandou

Open Access

https://doi.org/10.3390/universe8020117

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Abstract

For a pure SU(2) Yang–Mills theory in 4D, we revisit the spatial (3D), ball-like region of radius r0 in its bulk subject to the pressureless, deconfining phase at T0=1.32Tc, where Tc denotes the critical temperature for the onset of the deconfining–preconfining phase transition. Such a region possesses finite energy density and represents the self-intersection of a figure-eight shaped center-vortex loop if a BPS monopole of core radius ∼r052.4, isolated from its antimonopole by repulsion externally invoked through a transient shift of (anti)caloron holonomy (pair creation), is trapped therein. The entire soliton (vortex line plus region of self-intersection of mass m0 containing the monopole) can be considered an excitation of the pressureless and energyless ground state of the confining phase. Correcting an earlier estimate of r0, we show that the vortex-loop self-intersection region associates to the central part of a(n) (anti)caloron and that this region carries one unit of electric U(1) charge via the (electric-magnetic dually interpreted) charge of the monopole. The monopole core quantum vibrates at a thermodynamically determined frequency ω0 and is unresolved. For a deconfining-phase plasma oscillation about the zero-pressure background at T=T0, we compute the lowest frequency Ω0 within a neutral and homogeneous spatial ball (no trapped monopole) in dependence of its radius R0. For R0=r0 a comparison of Ω0 with ω0 reveals that the neutral plasma oscillates much slower than the same plasma driven by the oscillation of a monopole core.

Highlights

The thermodynamical phase structure of a single SU(2) Yang-Mills theory (electricmagnetic dually interpreted with respect to U(1) ⊂ SU(2)), comprising deconfining and preconfining thermal ground states of finite energy densities and massive gaugefield excitations as well as an energyless and pressureless confining ground state, suggests the existence of a solitonic, stable particle with intriguing yet familiar properties
T0 = 1.32 Tc, where Tc is the boundary1 of the deconfining phase, the pressure vanishes with positive slope [1]
The electric charge of this region is carried by a trapped BPS monopole of mass mm m0 which is not resolved thermodynamically and orginated by large-holonomycaloron dissociation [3]

Summary

Introduction

The thermodynamical phase structure of a single SU(2) Yang-Mills theory (electricmagnetic dually interpreted with respect to U(1) ⊂ SU(2)), comprising deconfining and preconfining thermal ground states of finite energy densities and (partially) massive gaugefield excitations as well as an energyless and pressureless confining ground state, suggests the existence of a solitonic, stable particle with intriguing yet familiar properties. We discuss a few amendments to [7], where the above-sketched model for a charged lepton (idealised to be stable against weak decay) was introduced, and we address oscillation physics about temperature T0 of a neutral plasma ball to conclude that the contributions to the quantum mass of the soliton from low-lying frequencies of such spherically symmetric breathing modes are negligible.

Self-Intersection Region of a Figure-Eight Shaped Center-Vortex Loop

Lowest Spherically Symmetric Breathing Mode

Summary and Discussion