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G2 monopoles

We investigate some aspects of Bogomolny-Prasad-Sommerfield monopole solutions in the Yang-Mills-Higgs theory with exceptional gauge group $G_2$ spontaneously broken to $U(1)\times U(1)$. Corresponding homotopy group is $π_2\left(G_2/U(1)\times U(1)\right)$ and similar to the $SU(3)$ theory, the $G_2$ monopoles are classified by two topological charges $(n_1,n_2)$. In fundamental representation these yield a subset of $SO(7)$ monopole configurations. Through inspection of the structure of $Alg(G_2)$, we propose an extension of the Nahm construction to the $(n,1)_{G_2}$ monopoles. For $(1,1)_{G_2}$ monopole the Nahm data are written explicitly.