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.

20 pages, 1 figure, corrected some typos

References in corpus (4)

• Normalized Vacuum States in N = 4 Supersymmetric Yang--Mills Quantum Mechanics with Any Gauge Group
• Orientifolds and twisted boundary conditions
• Numerical analysis of fractional charge solutions on the torus
• On flat connections with non-diagonalizable holonomies

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