Chern-Simons gauge theories, confinement, and the chiral spin liquid

Abstract

We reconsider the problem of confinement in theories with fermions with a compact gauge symmetry in 2+1 dimensions. We show that, as a result of the lack of gauge invariance of the determinant of the Dirac operator with a monopole background, the monopoles do not contribute to the Euclidean path integral. This result implies that fermions carrying the fundamental charge are not confined and that the spectrum of chiral-spin-liquid phases of theories of high-temperature superconductors supports separation of spin and charge.