arXiv 2409.014052024-09-07hep-thhep-ph

暗维度与力的大统一

The Dark Dimension and the Grand Unification of Forces

Jonathan J. Heckman, Cumrun Vafa, Timo Weigand, Fengjun Xu

备注：: 10 pages, 2 figures; v2: references added, typos corrected, minor corrections;

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AI总结：

本文在暗维度情景下研究规范力大统一，仅凭大统一假设与实验界限推出GUT标度、X玻色子质量及TeV级KK激发，并建立弱标度与GUT标度的关联。

摘要：

暗维度情景预言了一个微米量级的额外介观维度，它是通过将各种沼泽地原理应用于暗能量而提出的。在本短文中，我们发现在这一背景下实现规范力的大统一具有很强的约束性。我们并未实际构建任何GUT模型，而是论证：在此情景中，仅仅假设力的大统一，再结合对标准模型规范玻色子大质量复制品的实验界限，就预言了GUT标度的上限，即 $M_{GUT}\lesssim 10^{16}\\ {\rm GeV}$。结合质子寿命的实验界限，这预言介导质子衰变的 $X$ 规范玻色子是一根具有普朗克张力的5维孤立子弦，横跨长度标度 $L\sim ({\rm 1\\!-\\!10\\ TeV})^{-1}$，并终止于直径同样约为 $L$ 的规范膜上。由此得到质量 $M_X\sim 10^{15}\\!-\\!10^{16}\\ {\rm GeV}$。特别地，在暗维度情景中假设大统一，会导致规范膜上标准模型规范玻色子的Kaluza-Klein激发塔处于1–10 TeV范围。这表明规范膜的直径/间距 $L$ 同时与TeV附近的弱标度 $\sim 1/L$ 以及位于 $10^{16}\\ {\rm GeV}$ 的GUT标度 $\sim M_5^2 L$ 相关。

英文摘要：

The dark dimension scenario, predicting one extra mesoscopic dimension in the micron range, has emerged by applying various Swampland principles to the dark energy. In this note we find that realizing the grand unification of gauge forces is highly constraining in this context. Without actually constructing any GUT models, we argue that the mere assumption of grand unification of forces in this scenario, together with the experimental bounds on massive replicas of the Standard Model gauge bosons, predicts an upper bound for the GUT scale, $M_{GUT}\lesssim 10^{16}\ {\rm GeV}$. Combined with the experimental bound on the proton lifetime, this predicts that the $X$ gauge boson mediating proton decay is a 5d solitonic string of Planckian tension stretched across a length scale $L\sim ({\rm 1-10\ TeV})^{-1}$ ending on gauge branes of the same diameter $\sim L$. This leads to a mass of $M_X\sim 10^{15}-10^{16}\ {\rm GeV}$. In particular assuming grand unification in the dark dimension scenario results in a tower of Kaluza-Klein excitations of Standard Model gauge bosons on the gauge branes in the 1-10 TeV range. This suggests that the diameter/separation $L$ of the gauge branes correlates with both the weak scale $\sim 1/L$ near a TeV {\it and} the GUT scale $\sim M_5^2 L$ at $10^{16}\ {\rm GeV}$.

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