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In arXiv:0805.2192, we set up a gauge-theoretic equation on symplectic6-manifolds, which is a version of the Hermitian-Einstein equation perturbed byHiggs fields, and call Donaldson-Thomas equation, to analytically approach theDonaldson-Thomas invariants. In this article, we consider the equation oncompact K\"ahler threefolds, and study some of analytic properties of solutionsto them, using analytic methods in higher-dimensional Yang-Mills theorydeveloped by Nakajima and Tian with some additional arguments concerning anextra non-linear term coming from the Higgs fields. We prove that a sequence ofsolutions to the Donaldson-Thomas equation of a unitary vector bundle over acompact K\"ahler threefold has a converging subsequence outside a closed subsetwhose real 2-dimensional Hausdorff measure is finite, provided that theL^2-norms of the Higgs fields are uniformly bounded. We also prove ann/2-compactness theorem of solutions to the equations on compact K\"ahlerthreefolds.

A weak compactness theorem of the Donaldson-Thomas instantons on compact K\"ahler threefolds