等级问题与$\u003cspan style="font-style: italic; font-family: serif;"\u003eN\u003c/span\u003e=2$ $\u003cspan style="font-style: italic; font-family: serif;"\u003eD\u003c/span\u003e=5$超引力
The Hierarchy Problem and $\mathcal{N} =2$ $\mathcal{D} = 5$ Supergravity
AI总结：
本研究基于从11维紧致化得到的N=2五维超引力，提出解决等级问题的新方案，通过3-膜宇宙模型分析伸缩子与额外维度的关系，求解修正弗里德曼方程，给出两种额外维度标度下的卡鲁扎-克莱因激发特征。
摘要：
我们提出了一种解决等级问题的新方案，该方案基于从$\u003cspan style="font-style: italic; font-family: serif;"\u003eD\u003c/span\u003e=11$超引力紧致化在卡拉比-丘三维流形上得到的$\u003cspan style="font-style: italic; font-family: serif;"\u003eN\u003c/span\u003e=2$五维超引力。当将宇宙建模为嵌入五维体空间中的3-膜时，背景度规与超多重态场之一（即伸缩子，卡拉比-丘空间的体积模）成正比。求解伸缩子场方程时，我们发现它依赖于额外维度。我们求解了修正的弗里德曼方程，并得出该模型对膜上的有效四维引力标度与第五额外维度的普朗克标度（$\u003cspan style="font-style: italic; font-family: serif;"\u003eM\u003c/span\u003e$）之间关系的启示。我们考虑了两种不同的额外维度标度：第一种是额外维度处于太阳系尺度，且$\u003cspan style="font-style: italic; font-family: serif;"\u003eM\u003c/span\u003e$的量级为电弱标度；第二种是额外维度的标度量级为微米，且高维普朗克标度$\u003cspan style="font-style: italic; font-family: serif;"\u003eM\u003c/span\u003e \u0026sim; 10^{13} \u0026nbsp;\u0026text{GeV}$。在这两种情况下，卡鲁扎-克莱因激发的特征都与以往任何额外维度模型的特征截然不同。
英文摘要：
We introduce a new scenario to solve the hierarchy problem based on $\mathcal{N}=2$, five-dimensional supergravity compactified on Calabi-Yau threefold down from $\mathcal{D}=11$ supergravity. When modeling the universe as a 3-brane embedded in a five-dimensional bulk, the background metric is proportional to one of the hypermultiplets fields, namely the dilaton, the volume modulus of the Calabi-Yau space. When solving the dilaton field equation, we find that it is dependent on the extra dimension. We solve the modified Friedmann equations and find the implications of the model on the relation between the effective four-dimensional gravity scale in the brane and the Planck scale of the fifth extra dimension ($\mathcal{M} $). A couple of different scales are considered for the extra dimension, the first where the extra dimension is in range of the solar system and $\mathcal{M} $ is of order of the electroweak scale, and the second where the scale of the extra dimension is of order $μm$ and the higher dimensional Planck scale $\mathcal{M} \sim 10^{13} ~ \text{GeV}$. In both cases, the signatures of Kaluza-Klein excitations are quite distinct from the signatures of any previous extra dimensions model.
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