Two phases of topologically massive compact U(1) theory

The mean-field-like gauge-invariant variational method formulated recently is applied to topologically massive QED in three dimensions. We find that the theory has a phase transition in the Chern-Simons coefficient n. The phase transition is of the Berezinsky-Kosterlitz-Thouless type and is triggered by the liberation of Polyakov monopoles, which for n>8 are tightly bound into pairs. In our Hamiltonian approach this is seen as a similar behavior of the magnetic vortices, which are present in the ground state wave functional of the compact theory. For n>8, the low energy behavior of the theory is the same as in the noncompact case. For n<8 there are no propagating degrees of freedom on distance scales larger than the ultraviolet cutoff. The distinguishing property of the n<8 phase is that the magnetic flux symmetry is spontaneously broken.