Abstract
Generalized gauge fields with compact U(1) invariance of the “ lth” kind are examined by semiclassical methods. The technique is a direct generalization of Polyakov's for compact quantum electrodynamics. Suitable order parameters are defined, and it is found that these models are disordered for all couplings in l+1 dimensions, but possess a non-zero critical coupling in l+2 and higher dimensions. In particular this means that the U(1) rank-two antisymmetric tensor field in four dimensions has bubble-like particles, analogous to glueballs, in its spectrum, as well as a non-zero “surface tension”. The Z N models with compact invariance of the lth kind are shown to possess three phases in 2 l dimensions. The l+1 dimensional U(1) models contain spinless particles which are massless at the tree level, but develop a mass away from the fixed point due to instanton effects.
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