  Motivated by the high-T_c cuprates, we consider a model of bosonic Cooper
pairs moving on a square lattice via ring exchange. We show that this model
offers a natural middle ground between a conventional antiferromagnetic Mott
insulator and the fully deconfined fractionalized phase which underlies the
spin-charge separation scenario for high-T_c superconductivity. We show that
such ring models sustain a stable critical phase in two dimensions, the *Bose
metal*. The Bose metal is a compressible state, with gapless but uncondensed
boson and ``vortex'' excitations, power-law superconducting and charge-ordering
correlations, and broad spectral functions. We characterize the Bose metal with
the aid of an exact plaquette duality transformation, which motivates a
universal low energy description of the Bose metal. This description is in
terms of a pair of dual bosonic phase fields, and is a direct analog of the
well-known one-dimensional bosonization approach. We verify the validity of the
low energy description by numerical simulations of the ring model in its exact
dual form. The relevance to the high-T_c superconductors and a variety of
extensions to other systems are discussed, including the bosonization of a two
dimensional fermionic ring model.
