Abstract
The Sharpened Distance Conjecture and Tower Scalar Weak Gravity Conjecture are closely related but distinct conjectures, neither one implying the other. Motivated by examples, I propose that both are consequences of two new conjectures: 1. The infinite distance geodesics passing through an arbitrary point ϕ in the moduli space populate a dense set of directions in the tangent space at ϕ. 2. Along any infinite distance geodesic, there exists a tower of particles whose scalar-charge-to-mass ratio (–∇log m) projection everywhere along the geodesic is greater than or equal to \( 1/\sqrt{d-2} \). I perform several nontrivial tests of these new conjectures in maximal and half-maximal supergravity examples. I also use the Tower Scalar Weak Gravity Conjecture to conjecture a sharp bound on exponentially heavy towers that accompany infinite distance limits.
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Acknowledgments
I am especially grateful to my PhD advisor Ben Heidenreich for his mentorship. For feedback on the manuscript, I am grateful to Stephanie Baines, Gina Etheredge, Ben Heidenreich, Yue Qiu, Matthew Reece, Tom Rudelius, Ignacio Ruiz, Marin Sklan, and Flavio Tonioni. I have benefited from discussions with Philip Argyres, Stephanie Baines, Jacob McNamara, Yue Qiu, Muthusamy Rajaguru, Sebastian Rauch, Matthew Reece, Elias Riedel Gårding, Tom Rudelius, Ignacio Ruiz, Cumrun Vafa, Irene Valenzuela, and David Wu. Part of this work was done while at TASI, and part of this work was done during the 2023 Simons Summer Workshop at the Simons Center for Geometry and Physics, Stony Brook University. I received support from the NSF grant PHY-2112800.
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Etheredge, M. Dense geodesics, tower alignment, and the Sharpened Distance Conjecture. J. High Energ. Phys. 2024, 122 (2024). https://doi.org/10.1007/JHEP01(2024)122
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DOI: https://doi.org/10.1007/JHEP01(2024)122