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arXiv 2201.07177hep-th
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引力EFT上的(非)-投射界

(Non)-projective bounds on gravitational EFT

Li-Yuan Chiang, Yu-tin Huang, Wei Li, Laurentiu Rodina, He-Chen Weng

摘要:

在本文中,我们研究了四维引力有效场理论中的投影和非投影约束,这些约束来自于酉性、因果性和交叉性,假设$M_{\rm pl}$中的微扰UV完备化。利用数值半定规划和解析几何分析方法,我们从$R^3$和$D^{2n}R^4$的色散表示中推导出Wilson系数的界。从前者,我们得到的投影上的耦合比的界限,并观察聚点谱填充的允许区域的边界。对于后者,我们认为非射影几何的EFThedron,我们涉及到已知的$L$矩问题的文献。这使我们能够超越正性,并将上界从部分波的虚部的么正性。这导致了对各个系数的严格限制,这些系数在相对于UV尺度归一化时具有统一的阶数。最后,非射影几何也使我们能够得到最佳的界限反映低自旋优势的假设,改善以前的结果。我们补充了一个简单的线性规划方法,验证边界的分析。

英文摘要:

In this paper we study both projective and non-projective constraints on four-dimensional gravitational effective fields theories implied from unitarity, causality and crossing, assuming perturbative UV completions in $M_{\rm pl}$. We derive bounds on the Wilson coefficients of $R^3$ and $D^{2n}R^4$ from its dispersive representation, utilizing both numerical semi-definite programming and analytic geometry analysis. From the former, we derive projective bounds on ratios of couplings and observe accumulation point spectrum populating the boundary of the allowed region. For the latter we consider the non-projective geometry of the EFThedron, which we relate to the known $L$-moment problem in the literature. This allows us to move beyond positivity and incorporate the upper bound from unitarity of the imaginary parts of partial waves. This leads to sharp bounds on individual coefficients, which are of order unity when normalized with respect to the UV scale. Finally, the non-projective geometry also allows us to derive optimal bounds reflecting assumptions of low-spin dominance, improving previous results. We complement the analytic analysis with a simple linear programming approach that validates the bounds.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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