Galois symmetries in Super Yang-Mills Theories

Abstract

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.

arXiv comment30 pages; v2: typos corrected

References in corpus (6)

• Supersymmetric Yang-Mills Systems And Integrable Systems
• Dynamics of $SU(N)$ Supersymmetric Gauge Theory
• Phases of N=1 Supersymmetric Gauge Theories and Matrices
• Quantum parameter space and double scaling limits in N=1 super Yang-Mills theory
• Quantum parameter space in super Yang-Mills, II
• On the Geometry of Super Yang-Mills Theories: Phases and Irreducible Polynomials

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