The multicritical point principle as the origin of classical conformality and its generalizations
The multicritical point principle as the origin of classical conformality and its generalizations
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作为经典共形起源的多临界点原理及其推广
DOI：
10.1093/ptep/ptab161
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发表时间：
2021
影响因子：
3.5
通讯作者：
Kawana Kiyoharu
中科院分区：
文献类型：
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作者：
Kawai Hikaru;Kawana Kiyoharu
多临界点原理是一个有趣的理论可能性，可以解释宇宙的微调问题。它只是声称“一个理论的耦合常数被调谐到多临界点之一，在那里有效势的一些极值是退化的。”最简单的例子之一是有效势的二阶导数在最小值附近消失。这对应于所谓的经典保形性，因为它意味着重整化质量m2为零。更一般地说，模型的有效势的形式取决于几个耦合常数，我们应该扫描它们以找到所有的多临界点。研究了一般标量场在单圈水平上的多临界点，在此条件下，其它场的真空期望值均为零。为了简单起见，我们还假设其他场要么没有质量，要么太重，以至于它们对低能有效势没有贡献。这个假设使得我们的讨论非常简单，因为所得到的单圈有效势仅由四个有效耦合参数化。尽管由于假设的原因，我们的分析并不完全通用，但它仍然可以广泛适用于科尔曼-温伯格机制及其推广的许多模型。在对低能尺度下的多临界点进行分类之后，我们将简要地提到高能尺度下临界的可能性及其对宇宙学的影响。
The multicritical point principle is one of the interesting theoretical possibilities that can explain the fine-tuning problems of the universe. It simply claims that “the coupling constants of a theory are tuned to one of the multicritical points, where some of the extrema of the effective potential are degenerate.” One of the simplest examples is the vanishing of the second derivative of the effective potential around a minimum. This corresponds to the so-called classical conformality, because it implies that the renormalized massm2vanishes. More generally, the form of the effective potential of a model depends on several coupling constants, and we should sweep them to find all the multicritical points. We study the multicritical points of a general scalar field ϕ at one-loop level under the circumstance that the vacuum expectation values of the other fields are all zero. For simplicity, we also assume that the other fields are either massless or so heavy that they do not contribute to the low-energy effective potential of ϕ. This assumption makes our discussion very simple because the resultant one-loop effective potential is parametrized by only four effective couplings. Although our analysis is not completely general because of the assumption, it can still be widely applicable to many models of the Coleman–Weinberg mechanism and its generalizations. After classifying the multicritical points at low-energy scales, we will briefly mention the possibility of criticalities at high-energy scales and their implications for cosmology.