A remarkable picture of the underdoped cuprates has emerged
from recent quantum oscillation, high field transport, photoemission,
and STM experiments. A central feature is the "nodal-anti-nodal
dichotomy", the distinct behavior of the electronic excitations in different
regions of the Brillouin zone. I begin with a spin density wave (SDW) metal,
with electron and hole pockets, and present a theory of strong fluctuations
in the local orientation of the SDW order. When the global
SDW order vanishes, we obtain a novel quantum phase, the
"algebraic charge liquid", which has Fermi pockets interacting strongly via
an emergent collective gauge force. I discuss the pairing instabilities of these
metals, using analogies to double layer quantum Hall systems.
This theory leads
naturally to a d-wave superconductor with very different pairing properties
in the nodal and anti-nodal regions of the Brillouin zone.
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