Abstract
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) 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.
Highlights
It does not mean that an action does not exist, though it does mean that the action will be of limited use, probably no more than giving the corresponding equation of motion. This is still very interesting since one can expect that nontrivial spacetime physics of M-theory could be learned from the physics of the solitonic objects of the worldvolume theory of M5-branes, much like the cases of M2-branes and D-branes
Our convention for the Lie algebra are: [T a, T b] = if abcT c, Fμν = iFμaνT a, Aμ = iAaμT a and Fμaν = ∂μAaν − ∂ν Aaμ − f abcAbμAcν. Evidence that this self-duality equation describes the physics of multiple M5-branes was provided in [1], and further in [21,22,23]
A general feature of the non-abelian monopole is that the gauge symmetry G is broken down asymptotically to a little group H by the large r values of the scalar field Φ
Summary
Our convention for the Lie algebra are: [T a, T b] = if abcT c, Fμν = iFμaνT a, Aμ = iAaμT a and Fμaν = ∂μAaν − ∂ν Aaμ − f abcAbμAcν Evidence that this self-duality equation describes the physics of multiple M5-branes was provided in [1], and further in [21,22,23]. This result is potentially interesting as, given this rather explicit connection between BPS monopole and self-dual string, one may be able to provide a Nahm like construction for non-abelian self-dual string, which has been speculated and analyzed by other authors [25].
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