The Moduli Space Curvature and the Weak Gravity Conjecture
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| Format: | Preprint |
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2024
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| author | Castellano, Alberto Marchesano, Fernando Melotti, Luca Paoloni, Lorenzo |
| author_facet | Castellano, Alberto Marchesano, Fernando Melotti, Luca Paoloni, Lorenzo |
| contents | We unveil a remarkable interplay between rigid field theories (RFTs), charge-to-mass ratios $γ$ and scalar curvature divergences $\mathsf{R}_{\rm div}$ in the vector multiplet moduli space of 4d ${\cal N}=2$ supergravities, obtained upon compactifying type II string theory on Calabi--Yau threefolds. We show that the condition to obtain an RFT that decouples from gravity implies a divergence in the $γ$ of (would-be) BPS particles charged under the rigid theory, and vice-versa. For weak coupling limits, where the scalar curvature diverges, we argue that such BPS particles exist and that $\mathsf{R}_{\rm div} \lesssim γ^2$, implying that all these divergences are a consequence of RFT limits. More precisely, along geodesics we find that $\mathsf{R}_{\rm div} \sim (Λ_{\rm wgc}/Λ_g)^2$, where $Λ_{\rm wgc} \equiv g_{\rm rigid} M_{\rm Pl}$ is the RFT cut-off estimate of the Weak Gravity Conjecture and $Λ_g = g_{\rm rigid}^{-2} Λ_{\rm RFT}$ the electrostatic energy integrated up to its actual cut-off $Λ_{\rm RFT}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_10966 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Moduli Space Curvature and the Weak Gravity Conjecture Castellano, Alberto Marchesano, Fernando Melotti, Luca Paoloni, Lorenzo High Energy Physics - Theory We unveil a remarkable interplay between rigid field theories (RFTs), charge-to-mass ratios $γ$ and scalar curvature divergences $\mathsf{R}_{\rm div}$ in the vector multiplet moduli space of 4d ${\cal N}=2$ supergravities, obtained upon compactifying type II string theory on Calabi--Yau threefolds. We show that the condition to obtain an RFT that decouples from gravity implies a divergence in the $γ$ of (would-be) BPS particles charged under the rigid theory, and vice-versa. For weak coupling limits, where the scalar curvature diverges, we argue that such BPS particles exist and that $\mathsf{R}_{\rm div} \lesssim γ^2$, implying that all these divergences are a consequence of RFT limits. More precisely, along geodesics we find that $\mathsf{R}_{\rm div} \sim (Λ_{\rm wgc}/Λ_g)^2$, where $Λ_{\rm wgc} \equiv g_{\rm rigid} M_{\rm Pl}$ is the RFT cut-off estimate of the Weak Gravity Conjecture and $Λ_g = g_{\rm rigid}^{-2} Λ_{\rm RFT}$ the electrostatic energy integrated up to its actual cut-off $Λ_{\rm RFT}$. |
| title | The Moduli Space Curvature and the Weak Gravity Conjecture |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.10966 |