SUPERSYMMETRY IN THE 2-ANYON PROBLEM

We show that the problem of two anyons interacting through a simple harmonic potential or a Coulomb potential is supersymmetric. The supersymmetry operators map a theory described by statistics parameter theta to one described by pi + theta. Thus fermions and bosons go into each other, while semions are supersymmetric by themselves. The simple harmonic problem has a Sp(4) symmetry for any value of theta which explains the energy degeneracies.