Direct observation of string vibrations in three-dimensional compact QED

Three-dimensional compact U(1) is studied on a 16×32×16 lattice with emphasis on roughening around the crossover region. Configurations including two static charges are generated using the dual formulation of the theory. In this way the flux patterns between the charges are mapped out. Very convincing evidence for roughening is found. In particular we show that the average transverse spread of the flux tube follows a simple string model prediction as a function of charge separation. We also establish a nonvanishing string tension unambiguously. Its value turns out to be a factor two larger than what has been found in the more conventional Wilson loop approach.