An Effective Model for Glueballs and Dual Superconductivity at Finite Temperature

The glueballs lead to gluon and QCD monopole condensations as by-products of color confinement. A color dielectric function $G\left(\mid \varphi \mid \right)$ coupled with a Abelian gauge field is properly defined to mediate the glueball interactions at confining regime after spontaneous symmetry breaking (SSB) of the gauge symmetry. The particles are expected to form through the quark-gluon plasma (QGP) hadronization phase where the free quarks and gluons start clamping together to form hadrons. The QCD-like vacuum $〈{\eta }^2{m}_{\eta }^2{F}^{\mu \nu }{F}_{\mu \nu }〉$ , confining potential $V_c\left(r\right)$ , string tension $\sigma$ , penetration depth $\lambda$ , superconducting and normal monopole densities ( $n_s{n}_n$ ), and the effective masses ( $m_{\eta }^2$ and $m_A^2$ ) will be investigated at finite temperature $T$ . We also calculate the strong “running” coupling ${\alpha }_s$ and subsequently the QCD $\beta$ -function. The dual superconducting nature of the QCD vacuum will be investigated based on monopole condensation.