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arXiv 1812.06751hep-th
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多尺度重整化群方程下$β$函数的梯度流

Gradient flows for $β$ functions via multi-scale renormalization group equations

Ulrich Ellwanger

摘要:

重整化方案和截断方案允许为不同的耦合引入各种不同的重整化标度。我们考虑几个边缘耦合的耦合重整化群流,这些耦合依赖于同样多的重整化标度。通常的$β$函数描述的流动相对于一个共同的全球规模被假定为给定的。在这个框架内,人们总是可以在耦合空间中构造度量和势,使得$β$函数可以表示为势的梯度。此外,势本身可以明确地从一个前势导出,而前势又决定了度量。重整化群流的一些例子被认为是,和度量和潜力相比,在其他地方获得的表达式。

英文摘要:

Renormalization schemes and cutoff schemes allow for the introduction of various distinct renormalization scales for distinct couplings. We consider the coupled renormalization group flow of several marginal couplings which depend on just as many renormalization scales. The usual $β$ functions describing the flow with respect to a common global scale are assumed to be given. Within this framework one can always construct a metric and a potential in the space of couplings such that the $β$ functions can be expressed as gradients of the potential. Moreover the potential itself can be derived explicitly from a prepotential which, in turn, determines the metric. Some examples of renormalization group flows are considered, and the metric and the potential are compared to expressions obtained elsewhere.

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