We present and discuss explicit solutions to the non-Abelian self-dual string equation as well as to the non-Abelian self-duality equation in six dimensions. These solutions are generalizations of the ’t Hooft–Polyakov monopole and the basic SU(2) instanton to higher gauge theory. We expect that these solutions are relevant to the effective description of M2- and M5-branes.

• Received 27 January 2014

DOI:https://doi.org/10.1103/PhysRevD.89.065036