论文标题
模量依赖物种量表
Moduli-dependent Species Scale
论文作者
论文摘要
重力理论中光模式数量的计数是由“物种量表”的概念捕获的，该概念在Planck量表以下是有效的紫外线截止。我们建议在4D的背景下定义一个依赖模量的物种量表，$ {\ cal n} = 2 $理论，使用一个循环拓扑自由能$ f_1 $，我们将其与$ a $ a $ function的重力版本有关。这导致$λ_ {\ rm sp} \ sim 1/\ sqrt {f_1} $从Moduli空间的各个角落中恢复物种规模的预期缩放。此外，通过最小化$ f_1 $，我们将Moduli空间（“沙漠点”）的中心定义为物种规模最大的点。在这一点上，轻度自由度的数量被最小化。
The counting of the number of light modes in a gravitational theory is captured by the notion of the `species scale', which serves as an effective UV cutoff below the Planck scale. We propose to define a moduli-dependent species scale in the context of 4d, ${\cal N}=2$ theories, using the one loop topological free energy $F_1$, which we relate to a gravitational version of the $a$-function. This leads to $Λ_{\rm sp}\sim 1/\sqrt{F_1}$ from which we recover the expected scaling of the species scale in various corners of the moduli space. Moreover by minimizing $F_1$ we define the center of the moduli space (the `desert point') as a point where the species scale is maximal. At this point the number of light degrees of freedom is minimized.
