Gauge invariance of fractionally charged quasiparticles and hidden topological Zn symmetry

Using the braid-group formalism we study the consequences of gauge invariance for fractionally charged anyonic quasiparticles in a two-dimensional multiply connected system. It is shown that gauge invariance requires multicomponent wave functions, and leads to the emergence of a hidden topological Zn symmetry with associated quantum number and unavoidable occurrence of level crossings for manybody eigenstates. In certain situations, it relates the fractional charge to anyon statistics. The implications for the fractional quantum Hall effect are also discussed.