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 $1/(\tau-\tau')^2$ 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 co-efficient which has a finite enhancement near the quantum critical point.
Highlights
Coupled gauge theories in 2+1 space-time dimensions play a fundamental role in many phenomena in quantum condensed matter physics
We examine here further aspects of a recently proposed [15,16] SU(2) gauge theory for the vicinity of optimal doping in which a parent conformal theory is coupled to a large Fermi surface of gauge-neutral electrons
Expansion, where Nh is the number of flavors of Higgs fields, we find that this long-range interaction leads to a field theory that is bilocal in time, but local in space, i.e., some fields depend upon one spatial coordinate x, and two time coordinates τ and τ
Summary
Coupled gauge theories in 2+1 space-time dimensions play a fundamental role in many phenomena in quantum condensed matter physics. The best understood class of such critical points have an emergent relativistic conformal symmetry, allowing use of many tools from the conformal field theory literature Such conformal gauge theories apply to limited classes of phenomena in insulators or quantum Hall systems, and usually not to metallic, compressible systems with Fermi surfaces in the clean limit. In the vicinity of conventional symmetry breaking transitions, Hertz [25] argued that the low energy excitations on the Fermi surface could be accounted for by long-range interactions between the order parameter fields. Such arguments were extended to the SU(2) gauge theory in Ref. IV, where we will obtain some results to order 1/Nh, including the value of z in Eq (75)
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