Renormalization of strongly coupled U(1) lattice gauge theories

Recent numerical studies of the 4D pure compact U(1) lattice gauge theory, I have participated in, are reviewed. We look for a possibility to construct an interesting nonperturbatively renormalizable continuum theory at the phase transition between the confinement and Coulomb phases. First I describe the numerical evidence, obtained from calculation of bulk observables on spherical lattices, that the theory has a non-Gaussian fixed point. Further the gauge-ball spectrum in the confinement phase is presented and its universality confirmed. The unexpected result is that, in addition to massive states, the theory contains a very light, possibly massless scalar gauge ball. I also summarize results of studies of the compact U(1) lattice theory with fermion and scalar matter fields and point out that at strong coupling it represents a model of dynamical fermion mass generation.