Abstract
We show that in the neighborhood of a negative coordinate axis, the U(1) sector of the static dyonic solutions to the noncommutative U(4) N=4 super Yang–Mills (SYM) can be consistently decoupled from the SU(4) to all orders in the noncommutativity parameter. We show the above decoupling in two ways. First, we show the noncommutative dyon being the same as the commutative dyon, is a consistent solution to noncommutative equations of motion in the abovementioned region of noncommutative space. Second, as an example of decoupling of a non-null U(1) sector, we also obtain a family of solutions with nontrivial U(1) components for all components of the gauge field in the same region of noncommutative space. In both cases, the SU(4) and U(1) components separately satisfy the equations of motion.
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