Instantons at Angles

We find solutions of the Yang-Mills field equations with gauge group SU(2) in 4k dimensions which have the interpretation of four-dimensional instantons at angles. These configurations satisfy a BPS-like condition which arises in the context of two-dimensional (4,0)-supersymmetric sigma models. Moreover we show that these solutions are examples of Hermitian-Einstein connections on E. In the past twenty years, much work has been done to find classical solutions of the Yang-Mills field equations and to interpret them in the context of classical or quantum theory. A particular class of such configurations are the so called BPS ones. These configurations saturate a bound and when embedded in a supersymmetric extension of the Yang-Mills theory preserve a proportion of the supersymmetry. Examples of such configurations in four dimensions are the BPS monopoles and instantons. The former configurations saturate a bound for the energy of a Yang-Mills theory coupled to scalars in the adjoint representation of the gauge group while the latter configurations saturate a bound for the Euclidean action of the Yang-Mills theory. Instantons configurations are characterized by the first Pontryagin number, ν, and obey the antiself-duality condition ⋆