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In this Letter we point out that the analytic solution of the two dimensional U(1) gauge theory, on a finite lattice, reveals in the continuum limit the renowned Manton's spectrum of topological electric fluxes together with their effective hamiltonian and wave functions. We extend this result for the system with strings and external charges providing also a novel interpretation of the theta parameter. Some further generalizations are also outlined.doi:10.5506/aphyspolb.44.713 fatcat:ov2n76ulizbuxgiz6l6jga4g7i