Dynamics of non-integrable phases and gauge symmetry breaking

• Published in: Annals of physics 1989-03, Vol.190 (2), p.233-253
• Main Author: Hosotani, Yutaka
• Format: Article
• Language: English
• Subjects: Classical and quantum physics: mechanics and fields; Exact sciences and technology; Physics; Theory of quantized fields
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/0003-4916(89)90015-8

On a multiply-connected space the non-integrable phase factor P exp(ig ∫ A μ dx μ }, a pathordered line integral along a non-contractable loop, becomes a dynamical degree of freedom in gauge theory. The dynamics of such non-integrable phases are examined in detail with the most general boundary condition for gauge fields and fermions. Sometimes the dynamics of the non-integrable phases compensate the arbitrariness in the boundary condition imposed, leading to the same physics results. In other cases the dynamics of the non-integrable phases induce spontaneous breaking of non-Abelian gauge symmetry. In other words the physically realized symmetry of the system differs from, and can be either greater or smaller than, the symmetry of the boundary condition. The effective potential for the non-integrable phases in the SU( N) gauge theory on S 1 ⊗ R 1, d−2 is computed in the one-loop approximation. It is shown that the gauge symmetry is dynamically broken in the presence of fermions in the adjoint representation, depending on the value of the boundary condition parameter.