  We describe two dimensional models with a metallic Fermi surface which
display quantum phase transitions controlled by strongly interacting critical
field theories below their upper critical dimension. The primary examples
involve transitions with a topological order parameter associated with
dislocations in collinear spin density wave ("stripe") correlations: the
gapping of the order parameter fluctuations leads to a fractionalization of
spin and charge collective modes, and this transition has been proposed as a
candidate for the cuprates near optimal doping. The coupling between the order
parameter and long-wavelength volume and shape deformations of the Fermi
surface is analyzed by the renormalization group, and a runaway flow to a
non-perturbative regime is found in most cases. A phenomenological scaling
analysis of simple observable properties of possible second order quantum
critical points is presented, with results quite similar to those near quantum
spin glass transitions and to phenomenological forms proposed by Schroeder et
al. (cond-mat/0011002).
