Non-abelian self-dual strings in six dimensions from four dimensional 1/2-BPS monopoles

We explain a new construction of self-dual string solutions to the non-abelian two-form self-duality equation proposed in [1]. This class of self-dual strings is determined by the BPS monopoles in four-dimensions and the self-dual string charge is given by the charge of the monopole. Our construction covers the SO(4)SO(4) invariant self-dual string solutions found previously. We have also constructed, based on the 't Hooft–Polyakov monopole, a singular solution that describes two finitely separated M5-branes meeting midway in between. We comment that as BPS monopoles are generally given by the Nahm construction, our construction suggests that a generalized Nahm transform may exist for the non-abelian self-dual strings.