Perturbative Critical Behavior from Spacetime Dependent Couplings
Perturbative Critical Behavior from Spacetime Dependent Couplings
复制标题
时空相关耦合的微扰临界行为
DOI：
10.1103/physrevd.86.105028
复制
发表时间：
2012
影响因子：
5
通讯作者：
G. Torroba
中科院分区：
文献类型：
--
作者：
Xi Dong;B. Horn;E. Silverstein;G. Torroba
我们发现新的微扰不动点通过引入温和的时空依赖耦合到其他边际项。在四维量子傅立叶变换中，这些是小的威尔逊-费希尔不动点的物理类似物。我们没有考虑4 - o维，而是在4维中引入了耦合，其主要时空依赖形式为λx κµκ，其中一个小参数κ的作用类似于o。我们表明，在φ 4理论和无质量的QED和QCD中，这导致了一个在时空位置x的指数宽窗口上的微扰控制下的临界理论。我们理论中的精确不动点耦合λ∗(x)与平移不变理论的运行耦合相同，尺度由1/x代替。类似的陈述也适用于三维φ 6理论和具有弯曲目标空间的二维sigma模型。我们也用共形摄动理论描述了强耦合的例子。
We find novel perturbative fixed points by introducing mildly spacetime-dependent couplings into otherwise marginal terms. In four-dimensional QFT, these are physical analogues of the small-ǫ Wilson-Fisher fixed point. Rather than considering 4 − ǫ dimensions, we stay in four dimensions but introduce couplings whose leading spacetime dependence is of the form λx κ µ κ , with a small parameter κ playing a role analogous to ǫ. We show, in φ 4 theory and in QED and QCD with massless flavors, that this leads to a critical theory under perturbative control over an exponentially wide window of spacetime positions x. The exact fixed point coupling λ∗(x) in our theory is identical to the running coupling of the translationally invariant theory, with the scale replaced by 1/x. Similar statements hold for three-dimensional φ 6 theories and two-dimensional sigma models with curved target spaces. We also describe strongly coupled examples using conformal perturbation theory.