G2 monopoles

Ya Shnir; G. Zhilin

arXiv:1508.01871·hep-th·September 2, 2015

G2 monopoles

Ya Shnir, G. Zhilin

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TL;DR

This paper explores monopole solutions in the exceptional gauge group G2 within Yang-Mills-Higgs theory, classifies them by topological charges, and extends the Nahm construction to these monopoles, providing explicit data for the (1,1) case.

Contribution

It introduces an extension of the Nahm construction specifically for G2 monopoles and provides explicit solutions for the (1,1) monopole configuration.

Findings

01

G2 monopoles classified by two topological charges

02

Extension of Nahm construction to G2 monopoles

03

Explicit Nahm data for (1,1) G2 monopole

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 $π_{2} (G_{2} / U (1) \times U (1))$ and similar to the $S U (3)$ theory, the $G_{2}$ monopoles are classified by two topological charges $(n_{1}, n_{2})$ . In fundamental representation these yield a subset of $S O (7)$ monopole configurations. Through inspection of the structure of $A l g (G_{2})$ , 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.

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