Oblique confinement and phase transitions in Chern-Simons gauge theories.

We investigate non-perturbative features of a planar Chern-Simons gauge theory modeling the long-distance physics of quantum Hall systems, including a finite gapM for excitations. By formulating the model on a lattice we identify the relevant topological configurations and their interactions. For M > Mcr, the model exhibits an oblique confinement phase, which we identify with Laughlin’s incompressible quantum fluid. For M < Mcr, we obtain a phase transition to a Coulomb phase or a confinement phase, depending on the value of the electromagnetic coupling.