Ersatz Fermi Liquid Universality Conjecture

Establish whether every non-Fermi liquid metal with microscopic lattice translation symmetry (i.e., clean systems without impurities) is an ersatz Fermi liquid, meaning it exhibits an emergent LU(1) symmetry associated with conservation of charge around the Fermi surface and a nonzero LU(1) 't Hooft anomaly coefficient.

Background

The review introduces the concept of an ersatz Fermi liquid: a compressible metallic state whose low-energy effective theory has an emergent LU(1) symmetry and a nonzero 't Hooft anomaly. This framework captures many exact, non-perturbative properties of metals without requiring quasiparticles and extends beyond conventional Fermi liquid theory.

The author discusses a conjecture that all clean, translation-invariant non-Fermi liquid metals are ersatz Fermi liquids. The motivation includes compressibility considerations and matching conditions between microscopic filling and emergent anomaly, which suggest that finite-dimensional internal symmetry groups are incompatible with irrational fillings, pointing toward an infinite-dimensional symmetry such as LU(1). Despite these arguments, a rigorous proof remains lacking.