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Compact abelian gauge theories in $d=2+1$ dimensions arise often as aneffective field-theoretic description of models of quantum insulators. In thispaper we review some recent results about the compact abelian Higgs model in$d=2+1$ in that context.Comment: 5 pages, 3 figures; based on talk by F.S. Nogueira in the Aachen  HEP2003 conferenc

Compact U(1) gauge theories in 2+1 dimensions and the physics of low dimensional insulating materials