Inspired by the cuprate stripes, we consider the problem of a one-dimensional metal living on a delocalized trajectory in two dimensional space: the metallic lattice string. A model is constructed with maximal coupling between longitudinal and transversal charge motions, which nevertheless renormalizes into a minimal generalization of the Luttinger liquid: an independent set of string modes has to be added to the long-wavelength theory, with a dynamics governed by the quantum sine-Gordon model.
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Zaanen et al. (1998) studied this question.
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