Bilocal quantum criticality

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/(tau - tau ')(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/(tau - tau')(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.