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The non-abelian Higgs (NAH) theory is studied in a strong magnetic field. Forsimplicity, we study the SU(2) NAH theory with the Higgs triplet in a constantstrong 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 photonfield $A_\mu$ remains to be massless. In a strong constant magnetic field nearand below the critical value $eB_c \equiv M^2$, the charged vector fields$A_\mu^\pm$ behave as 1+1-dimensional quasi-massless fields, and give a strongcorrelation along the magnetic-field direction between off-diagonal chargescoupled with $A_\mu^\pm$. This may lead a new type of confinement caused bycharged vector fields $A_\mu^\pm$.

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