G2 monopoles

Abstract

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 ${\pi }_2\left(G_2/U(1)\times U(1)\right)$ 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.

11 pages, 2 figures, to appear in Phys. Rev. D

References in corpus (4)

• Magnetic Monopole Dynamics, Supersymmetry, and Duality
• G_2 gauge theory at finite temperature
• Casimir Scaling and String Breaking in G(2) Gluodynamics
• Topological aspects of G2 Yang-Mills theory

Cited by in corpus (3)

• Low-Energy Dynamics of 3d $\mathcal{N}=2$ $G_2$ Supersymmetric Gauge Theory
• Cho decomposition, Abelian gauge fixing and monopoles in G(2) Yang-Mills theory
• The Structure Constants of the Exceptional Lie Algebra ${\mathfrak{g}}_2$ in the Cartan-Weyl Basis