Effective Lagrangian for holes in the spin-liquid state

Applying methods of nonlinear {σ} models, we propose an effective Lagrangian of holes in a spin-liquid state based on the Hubbard model. We study some dynamical properties of the holes especially those related to high-Tc superconductivity using the effective Lagrangian. We argue that there is an attractive interaction between holes in the spin-liquid state, at least in the large-N limit.