Helical Luttinger Liquids and Three Dimensional Black Holes

TL;DR

This paper establishes a theoretical connection between helical Luttinger liquids and fermions near 3D black holes using AdS/CFT, revealing universal features of strongly coupled quantum liquids with gravity duals.

Contribution

It demonstrates an explicit, string-theory-embeddable correspondence between strongly coupled 2D Luttinger liquids and 3D black hole geometries via AdS/CFT.

Findings

Green function near black hole horizon matches Luttinger liquid behavior

Universal low-energy structure for charged quantum liquids with gravity duals

Explicit microscopic Lagrangian for the Luttinger liquids

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.