We discover a low-energy equivalence between two apparently unrelated Lagrangians with fractional statistics. Exploiting this equivalence, we are able to study the quantum disordered phase of the nonlinear σ model with Hopf term. We find that the quasiparticles in the disordered phase also have fractional statistics. There appears to be a dual relationship between the ordered and disordered phases.

• Received 29 September 1988

DOI:https://doi.org/10.1103/PhysRevLett.62.1937