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Bounds on Field Range for Slowly Varying Positive Potentials
- Publication Year :
- 2023
-
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.<br />Comment: v2: 15 pages, 4 figures, references updated
- Subjects :
- High Energy Physics - Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2305.07701
- Document Type :
- Working Paper