Explicit Derivation of Yang-Mills Self-Dual Solutions on non-Commutative Harmonic Space

Details Explicit Derivation of Yang-Mills Self-Dual Solutions on non-Commutative Harmonic Space Explicit Derivation of Yang-Mills Self-Dual Solutions on non-Commutative Harmonic Space

2000-07-17

arxiv.org/abs/hep-th/0007137v1

Class.Quant.Grav. 18 (2001) 2339-2358

Physics

High Energy Physics

High Energy Physics - Theory

latex, 25 pages

Scientific paper

10.1088/0264-9381/18/12/309

We develop the noncommutative harmonic space (NHS) analysis to study the problem of solving the non-linear constraint eqs of noncommutative Yang-Mills self-duality in four-dimensions. We show that this space, denoted also as NHS($\eta,\theta$), has two SU(2) isovector deformations $\eta^{(ij)}$ and $\theta^{(ij)}$ parametrising respectively two noncommutative harmonic subspaces NHS($\eta,0$) and NHS($0,\theta$) used to study the self-dual and anti self-dual noncommutative Yang-Mills solutions. We formulate the Yang-Mills self-dual constraint eqs on NHS($\eta,0$) by extending the idea of harmonic analyticity to linearize them. Then we give a perturbative self-dual solution recovering the ordinary one. Finally we present the explicit computation of an exact self-dual solution.

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