Classical Yang-Mills Vacua on T3 : Explicit Constructions
K. G. Selivanov, A. V. Smilga
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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