Conformal field theory approach to Fermi liquids and other highly entangled states

The Fermi surface may be usefully viewed as a collection of (1+1)-dimensional chiral conformal field theories. This approach permits straightforward calculation of many anomalous ground-state properties of the Fermi gas, including entanglement entropy and number fluctuations. The (1+1)-dimensional picture also generalizes to finite temperature and the presence of interactions. We argue that the low-energy entanglement structure of Fermi liquid theory is universal, depending only on the geometry of the interacting Fermi surface. We also describe three additional systems in 3+1 dimensions where a similar mechanism leads to a violation of the boundary law for entanglement entropy