  Fermionizing the charge sector and bosonizing the spin part in the SU(2)
slave-boson theory, we derive an effective field theory for dynamics of doped
holes in the antiferromagnetically correlated spin background, where spin
fluctuations are described by an SO(5) Wess-Zumino-Witten (WZW) theory while
dynamics of doped holes is characterized by QED$_{3}$ with a chemical potential
term. An important feature of our effective field theory is the coupling term
between valance bond fluctuations and doped holes. Considering that valance
bond fluctuations are deeply related with monopole excitations of staggered
U(1) gauge fields in the bosonic field theory for spin fluctuations, we
demonstrate that hole dynamics helps deconfinement of bosonic spinons near the
quantum critical point of the SO(5) WZW theory. We solve this effective field
theory in the Eliashberg framework, and find non-Fermi liquid physics in
thermodynamics and transport, where $z = 3$ criticality with dynamical exponent
$z$ plays an important role for hole dynamics. We discuss validity of our field
theory, applying it to a doped spin chain and comparing it with the
slave-fermion framework. Furthermore, we discuss instability of the anomalous
metallic phase against superconductivity and density waves of doped holes,
resulting from competition between gauge and valance bond fluctuations.
