Constructing the holographic realization of a Luttinger Liquid/ Low dimensional AdS/CMT

Abstract

Interacting fermions in 1+1 dimensions display behaviour distinct from their higher dimensional counterpart. There is an absence of quasi-particles, any individual excitation becomes collective. Through the method of bosonization the Luttinger model is exactly solvable. The resulting theory has correlation functions that have interaction-dependent scaling at 2k_{f}. The necessary ingredients to describe this system holographically will be discussed. Earlier studies have shown that 2k_{f} singularities are absent in the large N limit. Moving away from this limit allows quantum corrections in the bulk. The goal of this master thesis was to calculate a fermionic loop correction to the gauge field two-point function. Under some assumptions analytic results can be realized which allow for a possible holographic description of low dimensional condensed matter.