We study the gauge boson propagator in the dual Abelian Higgs theory which
confines electric charges. The confinement is due to dual Abrikosov-Nielsen
-Olesen strings. We show that the infrared double pole 1/(p(2))(2) in the p
ropagator is absent due to the confinement phenomenon. Instead, specific an
gular singularities signal the eventual set in of the confinement. These an
gular singularities are a manifestation of the confining strings. (C) 1999
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