Galois symmetries in Super Yang-Mills Theories

Details Galois symmetries in Super Yang-Mills Theories Galois symmetries in Super Yang-Mills Theories

2009-01-26

arxiv.org/abs/0901.4079v2

JHEP 0903:128,2009

Physics

High Energy Physics

High Energy Physics - Theory

30 pages; v2: typos corrected

Scientific paper

10.1088/1126-6708/2009/03/128

Classifying the phases of gauge theories is hindered by the lack of local order parameters. In particular, the standard Wilson's and 't Hooft's non-local order parameters are known to be insufficient to explain the existence of the plethora of phases that are found in supersymmetric gauge theories. Motivated by these observations, we reanalyze the concept of gauge symmetry breaking using Galois theory. Unlike the ordinary classical notion of unbroken gauge group, the Galois symmetry makes sense in the full quantum theory and must be a phase invariant. The algebraic structure underlying the space of vacua of supersymmetric gauge theories, that we have developed recently, is precisely designed to allow a rigorous mathematical implementation of these ideas.

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