Particle Vortex and Boson Fermion Dualities in 2+1 dimensions

Abstract

We motivate the particle-vortex duality and discuss the salient features of Chern-Simons matter theories and use the ideas to help build the boson-fermion dualities in 2+1D quantum field theory. The dynamics of the particle and vortex excitations, phases from renormalization group flows are discussed and shown to be identical on both sides of the duality. Chern-Simons theories and their novel physics in 2+1D is explored to bring about a change in statistics of particles. Using these ideas and after computing the quantum anomalies in 2+1D fermion theories, we propose the statements of abelian and non-abelian bosonization. We motivate the dual physics of the theories by comparing global symmetries, phases from RG flows and gauge-invariant operators on both sides of the duality. Finally, we introduce techniques to manipulate and generalize these dualities to non-abelian quiver theories.