As a quantum gravity cut-off, the species scale ${\mathrm{\Lambda }}_s$ gets naturally compared to the energy scale of a scalar potential V in an EFT. In this note, the species scale, its rate $|\nabla {\mathrm{\Lambda }}_s|/{\mathrm{\Lambda }}_s$ and their field dependence, to those of a scalar potential is compared. To that end, a string compactification leading to a scalar potential with the same properties as the species scale, namely, being positive, starting at a maximum in the bulk of field space and going asymptotically to zero is first identified. The trajectory followed in our 14-fields scalar potential is the steepest descent. Evaluating the rate $|\nabla V|/V$ along this path, a local maximum, or bump, a feature noticed as well for the species scale are observed. The origin of this bump for the scalar potential, and compare it to that of the species scale are investigated.

中文翻译：

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与标量潜力碰撞到物种规模

作为量子引力截止，物种尺度${\mathrm{\Lambda }}_s$可以自然地与EFT中标量势V的能量尺度进行比较。在本说明中，物种规模、其比率$|\nabla {\mathrm{\Lambda }}_s|/{\mathrm{\Lambda }}_s$并将它们的场依赖性与标量势的场依赖性进行比较。为此，首先确定了弦紧致化，导致标量势具有与物种尺度相同的属性，即为正，从大部分场空间中的最大值开始并渐近至零。我们的 14 场标量势所遵循的轨迹是最陡的下降。评估率$|\nabla V|/V$沿着这条路径，观察到局部最大值或凹凸，这是物种规模中也注意到的一个特征。研究了标量势的这种凹凸的起源，并将其与物种标度的凹凸进行比较。