arXiv 2007.037842020-07-07hep-thhep-ph

三维Yukawa模型和强、弱耦合下的CFTs

Three dimensional Yukawa models and CFTs at strong and weak couplings

Marcus Benghi Pinto

发表信息：: Phys. Rev. D 102, 065005 (2020)
DOI：: 10.1103/PhysRevD.102.065005

摘要：

在考虑所有耦合值的平均场框架下，分析了有限温度下的无质量三维Gross-Neveu-Yukawa（GNY）和Nambu-Jona-Lasinio-Yukawa（NJLY）模型.当狄拉克费米子的个数取为$N_f=1/4$（GNY）和$N_f=1/2$（NJLY）时，这些模型与具有立方超势和单超场的超对称Wess-Zumino（WZ）理论有关。在这种情况下，结果表明，强弱熵密度比从Stefan-Boltzmann值，在弱限制，在强耦合$s/s_{free}=31/35$。这个值与最近对具有四次超势和$N$超场的超对称$O(N)$ WZ模型应用大-$N$近似得到的值一致。当$N_f=0$时，如预期的那样，获得恢复在$O(N)$标量模型的上下文中预测的比率的$s/s_{free}=4/5$。然而，与$O(N)$ WZ模型相反，这里分析的简单Yukawa模型并不表现为所有耦合的CFTs，因为共形测量仅在极弱和极强的极限处完全消失，尽管声速表明，在中间耦合处的偏差似乎相当小。通过比较每种情况下的热质量行为，我们可以发现这种差异是这样的结果：在GNY/NJLY情况下，费米子质量对于所有耦合都为零，而在$O(N)$ WZ中，它只在弱极限和强极限处为零。另一方面，汤川玻色子无量纲质量显示出更普遍的行为，从$2 \ln [(1+\sqrt{5})/2]$，在无限耦合，为零（在消失耦合）。

英文摘要：

The massless three dimensional Gross-Neveu-Yukawa (GNY) and Nambu--Jona-Lasinio--Yukawa (NJLY) models at finite temperatures are analyzed within the mean field framework considering all coupling values. When the number of Dirac fermions is taken to be $N_f=1/4$ (GNY) and $N_f=1/2$ (NJLY) these models relate to the supersymmetric Wess-Zumino (WZ) theory with cubic superpotential and one superfield. In this case the results show that the strong-weak entropy density ratio decreases from the Stefan-Boltzmann value, in the weak limit, to $s/s_{free}=31/35$ at strong couplings. This value agrees with the one recently obtained by applying the large-$N$ approximation to the supersymmetric $O(N)$ WZ model with quartic superpotential and $N$ superfields. When $N_f=0$ one obtains $s/s_{free}=4/5$ recovering, as expected, the ratio predicted in the context of the $O(N)$ scalar model. However, contrary to the $O(N)$ WZ model the simple Yukawa models analyzed here do not behave as CFTs for all couplings since the conformal measure exactly vanishes only at the extreme weak and strong limits although the speed of sound indicates that the deviation, at intermediate couplings, appears to be rather small. By comparing the thermal masses behavior in each case one can trace this difference as being a consequence that in the GNY/NJLY case the fermionic mass vanishes for all couplings while within the $O(N)$ WZ it only vanishes at the weak and strong limits. On the other hand, the Yukawa bosonic dimensionless masses display a more universal behavior decreasing from $2 \ln [(1+\sqrt{5})/2]$, at infinite coupling, to zero (at vanishing coupling).

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