Vortex description of fractionalized phases in an exciton Bose condensate

As a sequel to the previous work [Phys. Rev. B 72, 235104 (2005)] we present a vortex description of the fractionalized phase in exciton Bose condensate. Magnetic flux line and monopole of the 3+1D emergent U(1) gauge theory are identified in the exciton picture. A bundle of vortex and antivortex pairs of all flavors of excitons corresponds to the magnetic flux line and a point at which the vortices and antivortices recombine is identified as magnetic monopole. This completes the magnetic sector of the low-energy excitation in the fractionalized phase. We also find that a different phase can occur where fractionalization coexists with the long-range order of exciton.