Abstract
We study the low-energy effective theory for a non-Fermi-liquid state in dimensions, where a transverse U(1) gauge field is coupled with a patch of Fermi surface with flavors of fermion in the large limit. In the low-energy limit, quantum corrections are classified according to the genus of the two-dimensional 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 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 limit. As a result, there are infinitely many quantum corrections that contribute to the leading frequency dependence of the Green’s function of fermion on the Fermi surface. On the contrary, the boson self-energy is not modified beyond the one-loop level and the theory is stable in the large limit. The nonperturbative nature of the theory also shows up in correlation functions of gauge-invariant operators.
13 More- Received 16 June 2009
DOI:https://doi.org/10.1103/PhysRevB.80.165102
©2009 American Physical Society