Explicit Non-Abelian Monopoles and Instantons in SU(N) Pure Yang-Mills Theory

It is well known that there are no static non-Abelian monopole solutions in pure Yang-Mills theory on Minkowski space R. We show that such solutions exist in SU(N) gauge theory on the spaces R × S and R × S × S with Minkowski signature (− + ++). In the temporal gauge they are solutions of pure Yang-Mills theory on T × S, where T is R or S. Namely, imposing SO(3)-invariance and some reality conditions, we consistently reduce the Yang-Mills model on the above spaces to a non-Abelian analog of the φ kink model whose static solutions give SU(N) monopole (-antimonopole) configurations on the space R × S via the abovementioned correspondence. These solutions can also be considered as instanton configurations of Yang-Mills theory in 2 + 1 dimensions. The kink model on R × S admits also periodic sphaleron-type solutions describing chains of n kink-antikink pairs spaced around the circle S with arbitrary n > 0. They correspond to chains of n static monopole-antimonopole pairs on the space R×S1×S2 which can also be interpreted as instanton configurations in 2+1 dimensional pure Yang-Mills theory at finite temperature (thermal time circle). We also describe similar solutions in Euclidean SU(N) gauge theory on S × S interpreted as chains of n instantonantiinstanton pairs. ∗ Supported in part by the Deutsche Forschungsgemeinschaft (DFG).