Classical Yang-Mills Vacua on $T^{3}$ : Explicit Constructions

K. G. Selivanov; A. V. Smilga

doi:10.1103/physrevd.63.125020

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arXiv · hep-th/0010243

Classical Yang-Mills Vacua on $T^{3}$ : Explicit Constructions

K. G. Selivanov·A. V. Smilga

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Abstract

Flat connections for unitary gauge groups on a 3--torus with twisted boundary conditions as well as recently discovered periodic nontrivial flat connections with ``nondiagonalizable'' triples of holonomies for higher orthogonal and exceptional groups are constructed explicitly in terms of Jacobi theta functions with rational characteristics. The (fractional) Chern-Simons numbers of these vacuum gauge field configurations are verified by direct computation.

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K. G. Selivanov, A. V. Smilga. 2001-09-12. Classical Yang-Mills Vacua on $T^{3}$ : Explicit Constructions. https://doi.org/10.1103/physrevd.63.125020

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