Bilocal quantum criticality

Understand

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.