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.

中文翻译：

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双局部量子临界

我们考虑2 + 1维共形规范理论与其他自由度的耦合，这些自由度会引起空间局部但时间较长的变化 $\mathrm{1个}/{（\tau -{\tau }^{\prime }）}^2$规范中立的本地运营商之间的交互。这些理论被认为可以描述最佳掺杂附近的空穴掺杂的铜酸盐。我们专注于SU（2）规范理论${ñ}_H$ 伴随的希格斯场的味道在希格斯和约束相之间经历了量子跃迁： $\mathrm{1个}/{（\tau -{\tau }^{\prime }）}^2$相互作用来自于观众的大费米电子表面。大${ñ}_H$扩展导致一种有效的动作，其中包含的字段在时间上是双局部的，而在空间上是局部的。我们在定单中找到一个强耦合的固定点$\mathrm{1个}/{ñ}_H$，具有动态临界指数 $ž>\mathrm{1个}$。我们表明，熵保留了超标度，但仍导致温度比热呈线性，其系数在量子临界点附近具有有限的增强。