Helical Luttinger Liquids and Three Dimensional Black Holes

Abstract

Cold interacting fermions in two dimensions form exactly solvable Luttinger liquids, whose characteristic scaling exponents differ from those of conventional Fermi liquids. We use the AdS/CFT correspondence to discuss an equivalence between a class of helical, strongly coupled Luttinger liquids and fermions propagating in the background of a 3D black hole. The microscopic Lagrangian is explicitly known and the construction is fully embeddable in string theory. The retarded Green function at low temperature and energy arises from the geometry very near the black hole horizon. This structure is universal for all cold, charged liquids with a dual description in gravity.

4 pages

References in corpus (5)

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• Near-horizon symmetries of extremal black holes
• A Non-Fermi Liquid from a Charged Black Hole; A Critical Fermi Ball
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• From Maxwell-Chern-Simons theory in $Ad{S}_3$ towards hydrodynamics in 1+1 dimensions
• Phase space holography with no strings attached
• Statistics and dynamics of the center of mass coordinate in a quantum liquid
• Luttinger liquid with complex forward scattering: robustness and Berry phase
• A Simple Derivation of Finite-Temperature CFT Correlators from the BTZ Black Hole
• Holographic conductivity of 1+1 dimensional systems in soft wall model