Non-Abelian Higgs Theory in a Strong Magnetic Field and Confinement

Abstract

The non-abelian Higgs (NAH) theory is studied in a strong magnetic field. For simplicity, we study the SU(2) NAH theory with the Higgs triplet in a constant strong magnetic field $\vec{B}$, where the lowest-Landau-level (LLL) approximation can be used. Without magnetic fields, charged vector fields $A_{\mu }^{\pm }$ have a large mass $M$ due to Higgs condensation, while the photon field $A_{\mu }$ remains to be massless. In a strong constant magnetic field near and below the critical value $e{B}_c\equiv M^2$, the charged vector fields $A_{\mu }^{\pm }$ behave as 1+1-dimensional quasi-massless fields, and give a strong correlation along the magnetic-field direction between off-diagonal charges coupled with $A_{\mu }^{\pm }$. This may lead a new type of confinement caused by charged vector fields $A_{\mu }^{\pm }$.

Comments: 8 pages, 2 figures