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We describe two dimensional models with a metallic Fermi surface whichdisplay quantum phase transitions controlled by strongly interacting criticalfield theories below their upper critical dimension. The primary examplesinvolve transitions with a topological order parameter associated withdislocations in collinear spin density wave ("stripe") correlations: thegapping of the order parameter fluctuations leads to a fractionalization ofspin and charge collective modes, and this transition has been proposed as acandidate for the cuprates near optimal doping. The coupling between the orderparameter and long-wavelength volume and shape deformations of the Fermisurface is analyzed by the renormalization group, and a runaway flow to anon-perturbative regime is found in most cases. A phenomenological scalinganalysis of simple observable properties of possible second order quantumcritical points is presented, with results quite similar to those near quantumspin glass transitions and to phenomenological forms proposed by Schroeder etal. (cond-mat/0011002).Comment: 16 pages, 4 figures; (v2) additional clarifying remark

Strongly coupled quantum criticality with a Fermi surface in two dimensions: Fractionalization of spin and charge collective modes