Bilocal quantum criticality

Abstract

We consider 2+1-dimensional conformal gauge theories coupled to additional degrees of freedom which induce a spatially local but long-range in time 1/(τ−τ^{′})^{2} interaction between gauge-neutral local operators. Such theories have been argued to describe the hole-doped cuprates near optimal doping. We focus on a SU(2) gauge theory with N_{h} flavors of adjoint Higgs fields undergoing a quantum transition between Higgs and confining phases: the 1/(τ−τ^{′})^{2} interaction arises from a spectator large Fermi surface of electrons. The large N_{h} expansion leads to an effective action containing fields which are bilocal in time but local in space. We find a strongly coupled fixed point at order 1/N_{h}, with dynamic critical exponent z>1. We show that the entropy preserves hyperscaling but nevertheless leads to a linear in temperature specific heat with a coefficient which has a finite enhancement near the quantum critical point.