The Peculiarity of a Negative Coordinate Axis in Dyonic Solutions of Noncommutative N=4 Super Yang-Mills

TL;DR

This paper demonstrates that in a specific negative coordinate region, the U(1) sector of noncommutative dyonic solutions in N=4 SYM can be decoupled from the SU(4) sector, with both sectors satisfying equations of motion independently.

Contribution

It shows the decoupling of U(1) and SU(4) sectors in noncommutative N=4 SYM solutions within a negative coordinate region, valid to all orders in noncommutativity.

Findings

U(1) sector decouples from SU(4) sector in a negative coordinate region.

Noncommutative dyons match commutative dyons in that region.

Existence of solutions with nontrivial U(1) components for all gauge fields.

Abstract

We show that in a certain region of a negative coordinate axis, the U(1amaharia) 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 {\it 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 that 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 {\it 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.