Gauge-independent Brout-Englert-Higgs mechanism and Yang-Mills theory with a gauge-invariant gluon mass term

Abstract

For the Yang-Mills theory coupled to a single scalar field in the fundamental representation of the gauge group, we present a gauge-independent description of the Brout-Englert-Higgs mechanism by which massless gauge bosons acquire their mass. The new description should be compared with the conventional gauge-dependent description relying on the spontaneous gauge symmetry breaking due to a choice of the non-vanishing vacuum expectation value of the scalar field. In this paper we focus our consideration on the fundamental scalar field which extends the previous work done for the Yang-Mills theory with an adjoint scalar field. Moreover, we show that the Yang-Mills theory with a gauge-invariant mass term is obtained from the corresponding gauge-scalar model when the radial degree of freedom (length) of the scalar field is fixed. The result obtained in this paper is regarded as a continuum realization of the Fradkin-Shenker continuity and Osterwalder-Seiler theorem for the complementarity between Higgs regime and Confinement regime which was given in the gauge-invariant framework of the lattice gauge theory. Moreover, we discuss how confinement is investigated through the gauge-independent Brout-Englert-Higgs mechanism by starting with the complementary gauge-scalar model.

21 pages, no figures; version published

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• Reflection positivity and complex analysis of the Yang-Mills theory from a viewpoint of gluon confinement
• $H(4)$ tensor representations for the lattice Landau gauge gluon propagator and the estimation of lattice artefacts
• Type of dual superconductivity for the $SU(2)$ Yang--Mills theory
• Magnetic monopoles in pure $SU(2)$ Yang--Mills theory with a gauge-invariant mass
• Gauge-independent transition separating confinement and Higgs phases in lattice SU(2) gauge theory with a scalar field in the fundamental representation
• Dyon in the $SU(2)$ Yang--Mills theory with a gauge-invariant gluon mass toward quark confinement
• The Scalar Mode of Gravity
• The Fröhlich-Morchio-Strocchi mechanism: A underestimated legacy