Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions

Understand

We study the low energy effective theory for a non-Fermi liquid state in 2+1 dimensions, where a transverse U(1) gauge field is coupled with a patch of Fermi surface with N flavors of fermion in the large N limit.

• In the low energy limit, quantum corrections are classified according to the genus of the 2d surface on which Feynman diagrams can be drawn without a crossing in a double line representation, and all planar diagrams are important in the leading order.
• The emerging theory has the similar structure to the four dimensional SU(N) gauge theory in the large N limit.
• Because of strong quantum fluctuations caused by the abundant low energy excitations near the Fermi surface, low energy fermions remain strongly coupled even in the large N limit.