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28 - The ’t Hooft–Polyakov Monopole Solution and Topology

from Part II - Solitons and Topology; Non-Abelian Theory

Published online by Cambridge University Press:  04 March 2019

Horaƫiu Năstase
Affiliation:
Universidade Estadual Paulista, São Paulo
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Summary

We study the 't Hooft-Polyakov monopole solution of the nonabelian Georgi-Glashow model, a model with the gauge group SU(2)=SO(3) and scalar fields in the 3 representation. After setting up the model, and finding the vacuum manifold, we solve for the monopole through an ansatz. We then study the topology of the solution through an analysis of homotopy groups. We derive a Bogomolnyi bound, and a BPS limit (for the scalar quartic coupling to vanish), in which we get linear BPS equations, which are solved exactly. The topology of the BPS monopole is compared with the topology of the Dirac monopole, and an embedding relation of the latter in the former is found.

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Publisher: Cambridge University Press
Print publication year: 2019

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