We consider 2+1-dimensional conformal gauge theories coupled to additional degrees of freedom which induce a spatially local but long-range in time $1/{(\tau -{\tau }^{\prime })}^2$ 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 $1/{(\tau -{\tau }^{\prime })}^2$ 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.

• Received 11 June 2020
• Accepted 5 August 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.033390

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Published by the American Physical Society