  A key prediction of the SO(5) theory is the antiferromagnetic vortex state.
Recent neutron scattering experiment on LSCO superconductors revealed enhanced
antiferromagnetic order in the vortex state. Here we review theoretical
progress since the original proposal and present a theory of static and dynamic
antiferromanetic vortices in LSCO superconductors. It is shown that the
antiferromagnetic region induced by the vortices can be greater than the
coherence length, due to the light effective mass of the dynamic
antiferromagnetic fluctuations at optimal doping, and close promixity to the
antiferromagentic state in the underdoped regime. Systematic experiments are
proposed to unambiguously determine that the field induced magnetic scattering
originates from the vortices and not from the bulk.
