AI 中文总结
本文证明了引力KK理论中最轻及更重KK引力子与标量耦合的质量比普适界，采用共形自举方法，基于自旋-2散射振幅求和规则完成推导。
AI 中文摘要
Mirbabayi和Villadoro已为引力卡鲁扎-克莱因（KK）理论中最轻标量场质量的普适上界提供了有力数值证据，该界指出质量为$m_1$的最轻KK引力子，必须与至少一个质量为$m_{\rm sc}$的标量耦合，满足$(m_{\rm sc}/m_1)^2 \leq 4/3$。本文采用共形自举方法，将其应用于有质量自旋-2散射振幅的求和规则，给出该界的证明。此外，本文还证明，每个质量为$m_n$的更重KK引力子，必须与至少一个质量为$m_{\rm sc}$的标量耦合，满足$(m_{\rm sc}/m_n)^2 < 36/25$。
英文摘要
Mirbabayi and Villadoro have provided strong numerical evidence for a universal upper bound on the mass of the lightest scalar field in gravitational Kaluza--Klein (KK) theories. This bound states that the lightest KK graviton, with mass $m_{1}$, must couple to at least one scalar with mass $m_{\rm sc}$ such that $(m_{\rm sc} /m_{1})^2 \leq 4/3$. We give a proof of this bound using the approach of the conformal bootstrap applied to sum rules for massive spin-2 scattering amplitudes. We additionally show that each heavier KK graviton, with mass $m_n$, must couple to at least one scalar with mass $m_{\rm sc}$ such that $(m_{\rm sc} /m_{n})^2 < 36/25$.
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