Magnetic monopoles vs. Hopf defects in the Laplacian (Abelian) gauge

Details Magnetic monopoles vs. Hopf defects in the Laplacian (Abelian) gauge Magnetic monopoles vs. Hopf defects in the Laplacian (Abelian) gauge

2000-07-15

arxiv.org/abs/hep-th/0007119v1

Nucl.Phys. B593 (2001) 545-561

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, 3 figures

Scientific paper

10.1016/S0550-3213(00)00635-0

We investigate the Laplacian Abelian gauge on the sphere S^4 in the background of a single `t Hooft instanton. To this end we solve the eigenvalue problem of the covariant Laplace operator in the adjoint representation. The ground state wave function serves as an auxiliary Higgs field. We find that the ground state is always degenerate and has nodes. Upon diagonalisation, these zeros induce toplogical defects in the gauge potentials. The nature of the defects crucially depends on the order of the zeros. For first-order zeros one obtains magnetic monopoles. The generic defects, however, arise from zeros of second order and are pointlike. Their topological invariant is the Hopf index S^3 -> S^2. These findings are corroborated by an analysis of the Laplacian gauge in the fundamental representation where similar defects occur. Possible implications for the confinement scenario are discussed.

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