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arXiv · 2305.07701

Bounds on Field Range for Slowly Varying Positive Potentials

Damian van de Heisteeg·Cumrun Vafa·Max Wiesner·David H. Wu
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Abstract

In the context of quantum gravitational systems, we place bounds on regions in field space with slowly varying positive potentials. Using the fact that $V<\Lambda_s^2$, where $\Lambda_s(\phi)$ 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: $\Delta \phi \leq a \log(1/V) +b$ in Planck units, where $a\leq \sqrt{(d-1)(d-2)}$, and $b$ is an $\mathcal{O}(1)$ 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 constant $b$, which we verify is $\mathcal{O}(1)$ and negative in all the examples we studied.

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Damian van de Heisteeg, Cumrun Vafa, Max Wiesner, David H. Wu. 2023-05-12. Bounds on Field Range for Slowly Varying Positive Potentials. https://arxiv.org/abs/2305.07701

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