Abstract

TheSU(N) Yang-Mills equations are considered in a four-dimensional Euclidean box with periodic boundary conditions (hypertorus). Gauge-invariant twists can be introduced in these boundary conditions, to be labeled with integersn μν (= −n μν ), defined moduloN. The Pontryagin number in this space is often fractional. Whenever this number is zero there are solutions to the equationsG μν =0 HereG μν is the covariant curl. When this number is not zero we find a set of solutions to the equations $$G_{\mu \nu } = \tilde G_{\mu \nu } $$ , provided that the periodsa μ of the box satisfy certain relations.

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