Effective theory of high-temperature superconductors

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General field theory of a fluctuating d-wave superconductor is constructed and proposed as an effective description of superconducting cuprates at low energies. The theory is used to resolve a puzzle posed by recent experiments on superfluid density in severely underdoped YBCO. In particular, the overall temperature dependence of the superfluid density at low dopings is argued to be described well by the strongly anisotropic weakly interacting three-dimensional Bose gas, and thus approximately linear in temperature with an almost doping-independent slope.