Phase transitions in ZN gauge theory and twisted ZN topological phases

We find a series of non-Abelian topological phases that are separated from the deconfined phase of Z(N) gauge theory by a continuous quantum phase transition. These non-Abelian states, which we refer to as the twisted Z(N) states, are described by a recently studied U(1) x U(1) (sic) Z(2) Chern-Simons (CS) field theory. The U(1) x U(1) (sic) Z(2) CS theory provides a way of gauging the global Z(2) electric-magnetic symmetry of the Abelian Z(N) phases, yielding the twisted Z(N) states. We introduce a parton construction to describe the Abelian Z(N) phases in terms of integer quantum Hall states, which then allows us to obtain the non-Abelian states from a theory of Z(2) fractionalization. The non-Abelian twisted Z(N) states do not have topologically protected gapless edge modes and, for N > 2, break time-reversal symmetry.