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  1. ; ; ; (, Journal of High Energy Physics)
    A<sc>bstract</sc> In a quantum theory of gravity, the species scale Λscan be defined as the scale at which corrections to the Einstein action become important or alternatively as codifying the “number of light degrees of freedom”, due to the fact that$$ {\Lambda}_s^{-1} $$ Λ s − 1 is the smallest size black hole described by the EFT involving only the Einstein term. In this paper, we check the validity of this picture in diverse dimensions and with different amounts of supersymmetry and verify the expected behavior of the species scale at the boundary of moduli space. This also leads to the evaluation of the species scale in the interior of the moduli space as well as to the computation of the diameter of the moduli space. We also find evidence that the species scale satisfies the bound$$ {\frac{\left|\nabla {\Lambda}_s\right|}{\Lambda_s}}^2\le \frac{1}{d-2} $$ ∇ Λ s Λ s 2 ≤ 1 d − 2 all over moduli space including the interior. 
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  2. ; ; ; (, Journal of High Energy Physics)
    A<sc>bstract</sc> In the context of quantum gravitational systems, we place bounds on regions in field space with slowly varying positive potentials. Using the fact that$$ V<{\Lambda}_s^2 $$ V < Λ s 2 , where Λs(ϕ) is the species scale, and the emergent string conjecture, we show this places a bound on the maximum diameter of such regions in field space: ∆ϕ≤alog(1/V) +bin Planck units, wherea≤$$ \sqrt{\left(d-1\right)\left(d-2\right)} $$ d − 1 d − 2 , andbis an 𝒪(1) number and expected to be negative. The coefficient of the logarithmic term has previously been derived using TCC, providing further confirmation. For type II string flux compactifications on Calabi-Yau threefolds, using the recent results on the moduli dependence of the species scale, we can check the above relation and determine the constantb, which we verify is 𝒪(1) and negative in all the examples we studied. 
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