An Introduction to the Confinement Problem by Jeff Greensite

Author:Jeff Greensite
Language: eng
Format: epub, pdf
ISBN: 9783030515638
Publisher: Springer International Publishing

9.4 The Abelian Projection

The example of monopole confinement in compact QED, in the Georgi-Glashow model, and in the Seiberg-Witten model, raises the hope that some similar mechanism might exist in pure gauge theories, or gauge theories without fundamental matter fields. To make this idea work, one has to identify an abelian subgroup of the gauge group, associated with the abelian magnetic monopole field. Since there is no elementary Higgs field in the adjoint representation, whose unitary gauge would single out an appropriate abelian subgroup, ‘t Hooft [25] suggested that a composite operator involving only gluonic fields, and behaving under a gauge transformation G(x) like a matter field in the adjoint representation, might serve the same purpose. For a matrix-valued operator X(x), the gauge transformation law would be

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