Vortex description of quantum Hall ferromagnets

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We study particle states of quantum Hall ferromagnet from the viewpoint of the incompressible fluid description. It is shown that phase space of Chern-Simons matrix theory which is an effective theory for the incompressible fluid is equivalent to moduli space of vortex theory. According to this correspondence, elementary excitations in vortex theory are identified as particle states in quantum Hall ferromagnet, and thus we propose that a pure electron state is absent from the strong coupling region but only a composite particle state is present.