论文标题
三个循环的远程多尺度模型
Long-range multi-scalar models at three loops
论文作者
论文摘要
我们计算具有一般四分之一相互作用的远程多尺度模型的三环β函数。模型的远距离性质在动力学术语中编码，带有laplacian的功率$ 0 <ζ<1 $，使Feynman图的计算比通常的短距离情况（$ζ= 1 $）要难得多。结果，先前的结果停止了两个循环，而六循环结果可用于短距离型号。我们将重新归一化组的分析推到三个循环，以$ε=4ζ-ζ-d $扩展为固定尺寸$ d <4 $，使用schwinger参数化中Feynman振幅的Mellin-Barnes表示。然后，我们将Beta函数专门针对具有不同对称组的各种模型：$ O（n）$，$（\ Mathbb {z} _2）_2）^n \ rtimes s_n $和$ o（n）\ times o（m）$。对于此类模型，我们计算固定点和关键指数。
We compute the three-loop beta functions of long-range multi-scalar models with general quartic interactions. The long-range nature of the models is encoded in a kinetic term with a Laplacian to the power $0<ζ<1$, rendering the computation of Feynman diagrams much harder than in the usual short-range case ($ζ=1$). As a consequence, previous results stopped at two loops, while six-loop results are available for short-range models. We push the renormalization group analysis to three loops, in an $ε=4ζ-d$ expansion at fixed dimension $d<4$, extensively using the Mellin-Barnes representation of Feynman amplitudes in the Schwinger parametrization. We then specialize the beta functions to various models with different symmetry groups: $O(N)$, $(\mathbb{Z}_2)^N \rtimes S_N$, and $O(N)\times O(M)$. For such models, we compute the fixed points and critical exponents.
