Abelian Projection on the Torus for general Gauge Groups

Details Abelian Projection on the Torus for general Gauge Groups Abelian Projection on the Torus for general Gauge Groups

1998-09-30

arxiv.org/abs/hep-th/9809209v2

Nucl.Phys. B548 (1999) 585-612

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, 6 figures, little changes in the references

Scientific paper

10.1016/S0550-3213(99)00146-7

We consider Yang-Mills theories with general gauge groups $G$ and twists on the four torus. We find consistent boundary conditions for gauge fields in all instanton sectors. An extended Abelian projection with respect to the Polyakov loop operator is presented, where $A_0$ is independent of time and in the Cartan subalgebra. Fundamental domains for the gauge fixed $A_0$ are constructed for arbitrary gauge groups. In the sectors with non-vanishing instanton number such gauge fixings are necessarily singular. The singularities can be restricted to Dirac strings joining magnetically charged defects. The magnetic charges of these monopoles take their values in the co-root lattice of the gauge group. We relate the magnetic charges of the defects and the windings of suitable Higgs fields about these defects to the instanton number.

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