Helical Luttinger Liquids and Three Dimensional Black Holes

Understand

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.