Fractionalization and confinement in the U(1) and $Z_2$ gauge theories of strongly correlated systems

Recently, we have elucidated the physics of electron fractionalization in strongly interacting electron systems using a $Z_2$ gauge theory formulation. Here we discuss the connection with the earlier U(1) gauge theory approaches based on the slave boson mean field theory. In particular, we identify the relationship between the holons and Spinons of the slave-boson theory and the true physical excitations of the fractionalized phases that are readily described in the $Z_2$ approach.