arXiv 2308.154202023-08hep-phastro-ph.COhep-th

与引力耦合的标量场的几何与幺正性

Geometry and unitarity of scalar fields coupled to gravity

Minxi He, Kohei Kamada, Kyohei Mukaida

备注：: 6+2 pages, 1 table

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AI总结：

针对标量场与引力非共形耦合时 Weyl 变换导致目标空间几何依赖参考系的问题，本文纳入度规共形模扩展目标空间，给出明显 Weyl 变换与场重定义不变的几何表述，并用散射振幅验证截断能标。

摘要：

我们以一种明显独立于参考系的方式，构建了与引力非共形耦合的标量场理论。诸如 $S$ 矩阵之类的物理量应当在场重定义下保持不变，因此可以由目标空间的几何来表示。然而，当考虑与引力的耦合时，由于与 Weyl 变换相关的冗余性，这种优雅的几何表述会变得模糊。著名的例子是 Higgs 暴胀，其中 Higgs 场的目标空间在 Jordan 参考系中是平坦的，但在 Einstein 参考系中却是弯曲的。此外，人们甚至可以证明，O$(N)$ 非线性 $σ$ 模型的任何几何都可以通过适当的 Weyl 变换而被平坦化。在这篇 Letter 中，我们通过纳入度规的共形模来扩展目标空间的概念，并表明这种扩展几何提供了一种紧凑的表述，它明显具有 Weyl 变换/场重定义不变性。我们将截断能标识别为扩展目标空间曲率平方根的倒数，并证实它与基于我们形式体系从二对二散射振幅得到的截断能标相一致。

英文摘要：

We formulate scalar field theories coupled non-conformally to gravity in a manifestly frame-independent fashion. Physical quantities such as the $S$ matrix should be invariant under field redefinitions, and hence can be represented by the geometry of the target space. This elegant geometric formulation, however, is obscured when considering the coupling to gravity because of the redundancy associated with the Weyl transformation. The well-known example is the Higgs inflation, where the target space of the Higgs fields is flat in the Jordan frame but is curved in the Einstein frame. Furthermore, one can even show that any geometry of O$(N)$ nonlinear $σ$ models can be flattened by an appropriate Weyl transformation. In this Letter, we extend the notion of the target space by including the conformal mode of the metric, and show that the extended geometry provides a compact formulation that is manifestly Weyl-transformation/field-redefinition invariant. We identify the cutoff scale with the inverse of square root of the extended target space curvature and confirm that it coincides with that obtained from two-to-two scattering amplitudes based on our formalism.

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