Gradient flow and the renormalization group
Gradient flow and the renormalization group
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DOI：
10.1093/ptep/pty081
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发表时间：
2018-05
影响因子：
3.5
通讯作者：
Y. Abe;M. Fukuma
中科院分区：
文献类型：
--
作者：
Y. Abe;M. Fukuma
我们研究了梯度流的重整化群（RG）结构。而不是使用原来的裸动作来生成流，我们建议在每个流时间使用有效的动作。我们写下来的标量场理论的基本方程，决定了行动的演变，并认为，该方程可以被视为RG方程，如果一个使场变量变换在每一步，使动力学项保持采取标准形式。我们考虑了方程的局部势近似（LPA），并表明结果具有费曼图的自然解释。我们做了一个$\vareps $扩展的LPA和表明，它再现的特征值的线性RG变换周围的高斯和威尔逊-费舍尔不动点的顺序为$\vareps $。
We investigate the renormalization group (RG) structure of the gradient flow. Instead of using the original bare action to generate the flow, we propose to use the effective action at each flow time. We write down the basic equation for scalar field theory that determines the evolution of the action, and argue that the equation can be regarded as a RG equation if one makes a field-variable transformation at every step such that the kinetic term is kept to take the canonical form. We consider a local potential approximation (LPA) to our equation, and show that the result has a natural interpretation with Feynman diagrams. We make an $\varepsilon$ expansion of the LPA and show that it reproduces the eigenvalues of the linearized RG transformation around both the Gaussian and the Wilson-Fisher fixed points to the order of $\varepsilon$.