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We study properties of instanton and monopole in an external chromomagneticfield. Generally, the 't Hooft ansatz is no longer a solution of the Yang-Millsfield equation in the presence of external fields. Therefore, we investigate astabilized instanton solution with minimal total Yang-Mills action in anontrivial topological sector. With this aim, we consider numericalminimization of the action with respect to the global color orientation, theanisotropic scale transformation and the local gauge-like transformationstarting from a simple superposed gauge field of the 't Hooft ansatz and theexternal color field. Here, the external color field is, for simplicity, chosento be a constant Abelian magnetic field along a certain direction. Then, the4-dimensional rotational symmetry O(4) of the instanton solution is reduced totwo 2-dimensional rotational symmetries $O(2)\times O(2)$ due to the effect ofa homogeneous external field. In the space $\mib{R}^{3}$ at fixed $t$, we finda quadrupole deformation of this instanton solution. In the presence of amagnetic field $\vec{H}$, a prolate deformation occurs along the direction of$\vec{H}$. Contrastingly, in the presence of an electric field $\vec{E}$ anoblate deformation occurs along the direction of $\vec{E}$. We further discussthe local correlation between the instanton and the monopole in the externalfield in the maximally Abelian gauge. The external field affects the appearanceof the monopole trajectory around the instanton. In fact, a monopole andanti-monopole pair appears around the instanton center, and this monopole loopseems to partially screen the external field.Comment: 15 pages,8 figure

Instanton and Monopole in External Chromomagnetic Fields