On the phenomenon of symmetry enhancement in abelian gauge theories

Abstract

Z N spin systems in 2 dimensions and gauge theories in 4 dimensions ( clock models) have an intermediate-coupling massless phase, which very much resembles the massless phase of the U(1) theories obtained in the N → ∞ limit. We investigate the question of whether this phenomenon, sometimes referred to as symmetry enhancement, really means that the superselection sectors of the Z N model are labelled by the representations of U(1) rather than those of Z N ⊂ U(1). For the gauge theory case, we discuss possible constructions of charged N finite energy states that are not in the vacuum sector. An actual proof for the existence of charged states labelled by the representations of a larger group than the defining gauge symmetry can be given in a technically simpler situation: we consider the massless phase of a Z-gauge theory (discrete Gaussian model); there a charged state of charge 2π exists, which has the vacuum quantum numbers with respect to the group Z of integers, but not with respect to the “enhaced” group R of real numbers.