Bags and confinement governed by spontaneous symmetry breaking of scale invariance

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A general coordinate invariant theory is constructed where confinement of gauge fields and gauge dynamics in general is governed by the spontaneous symmetry breaking (s.s.b.) of scale invariance. The model uses two measures of integration in the action, the standard √-g where g is the determinant of the metric and another measure Φ independent of the metric. To implement scale invariance, a dilaton field is introduced. Using the first-order formalism, curvature (ΦR and √-gR2 terms, gauge field term (Φ√-FμvaFαβ agmu; αgv β and √-g F μva Fαβag mu; αgv β and dilaton kinetic terms are introduced in a conformally invariant way. Exponential potentials for the dilaton break down (softly) the conformal invariance down to global scale invariance, which also suffers s.s.b. after integrating the equations of motion. The model has a well-defined flat space limit. As a result of the s.s.b. of scale invariance phases with different vacuum energy density appear. Inside the bags, that is in the regions of larger vacuum energy density, the gauge dynamics is normal, that is nonconfining, while for the region of smaller vacuum energy density, the gauge field dynamics is confining. Likewise, the dynamics of scalars, like would be Goldstone bosons, is suppressed inside the bags.

Original languageEnglish
Pages (from-to)4195-4220
Number of pages26
JournalInternational Journal of Modern Physics A
Issue number22
StatePublished - 10 Sep 2010


  • Bag model
  • Confinement
  • Gauge fields
  • Vacuum energy density dynamics


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