  We study how to incorporate Mott physics in the BCS-type superconductor,
motivated from the fact that high $T_c$ superconductivity results from a Mott
insulator via hole doping. The U(1) slave-rotor representation was proposed to
take local density fluctuations into account non-perturbatively, describing the
Mott-Hubbard transition at half filling. Since this decomposition cannot
control local pairing fluctuations, the U(1) slave-rotor representation does
not give a satisfactory treatment for charge fluctuations. Extending the U(1)
slave-rotor representation, we introduce an SU(2) slave-rotor representation to
allow not only local density fluctuations but also local pairing excitations.
We find an SU(2) slave-rotor gauge theory of the Hubbard model in terms of two
kinds of collective boson excitations associated with density and pairing
fluctuations that interact with gapless fermion excitations via SU(2) gauge
fluctuations. An interesting observation in this effective description is that
phase fluctuations of fermion pairs arise as SU(2) gauge fluctuations. Thus,
fermion-pairing excitations can be controlled by dynamics of collective bosons
in the SU(2) slave-rotor gauge theory. Performing the standard saddle-point
analysis based on the SU(2) slave-rotor action, we find ......
