SU(5) monopoles and the dual standard model

We find the spectrum of magnetic monopoles produced in the symmetry breaking $\mathrm{SU}\left(5\right)\to \left[\mathrm{SU}\right(3)\times \mathrm{SU}(2)\times \mathrm{U}(1{)}^{\prime }]{/Z}_6$ by constructing classical bound states of the fundamental monopoles. The spectrum of monopoles is found to correspond to the spectrum of one family of standard model fermions and, hence, is a starting point for constructing the dual standard model. At this level, however, there is an extra monopole state — the “diquark” monopole — with no corresponding standard model fermion. If the SU(3) factor now breaks down to $Z_3$, the monopoles with nontrivial SU(3) charge get confined by strings in SU(3) singlets. Another outcome of this symmetry breaking is that the diquark monopole becomes unstable (metastable) to fragmentation into fundamental monopoles and the one-one correspondence with the standard model fermions is restored. We discuss the fate of the monopoles if the $\left[\mathrm{SU}\right(2)\times \mathrm{U}(1{)}^{\prime }]{/Z}_2$ factor breaks down to U${\mathrm{}\left(1\right)\mathrm{}}_Q$ by a Higgs mechanism as in the electroweak model. Here we find that monopoles that are misaligned with the vacuum get connected by strings even though the electroweak symmetry breaking does not admit topological strings. We discuss the lowest order quantum corrections to the mass spectrum of monopoles.