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

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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Journal articles
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http://hal.in2p3.fr/in2p3-00193938
Contributor : Dominique Girod <>
Submitted on : Wednesday, December 5, 2007 - 10:47:21 AM
Last modification on : Thursday, February 7, 2019 - 2:57:46 PM

### Citation

K. G. Selivanov, A.V. Smilga. Classical Yang-Mills Vacua on $T^{3}$ : Explicit Constructions. Physical Review D, American Physical Society, 2001, 63, pp.125020. ⟨10.1103/PhysRevD.63.125020⟩. ⟨in2p3-00193938⟩

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