Abstract
The Distance Conjecture of Ooguri and Vafa holds that any infinite-distance limit in the moduli space of a quantum gravity theory must be accompanied by a tower of exponentially light particles, which places tight constraints on the low-energy effective field theories in these limits. One attempt to extend these constraints to the interior of moduli space is the refined Distance Conjecture, which holds that the towers of light particles predicted by the Distance Conjecture must appear any time a modulus makes a super-Planckian excursion in moduli space. In this note, however, we point out that a tower which satisfies the Distance Conjecture in an infinite-distance limit of moduli space may be parametrically heavier than the Planck scale for an arbitrarily long geodesic distance. This means that the refined Distance Conjecture, in its most naive form, does not place meaningful constraints on low-energy effective field theory. This motivates alternative refinements of the Distance Conjecture, which place an absolute upper bound on the tower mass scale in the interior of moduli space. We explore two possibilities, providing evidence for them and briefly discussing their implications.
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Acknowledgments
It is a pleasure to thank Ben Heidenreich for useful discussions. This work was supported in part by the Berkeley Center for Theoretical Physics; by the Department of Energy, Office of Science, Office of High Energy Physics under QuantISED Award DE-SC0019380 and under contract DE-AC02-05CH11231; and by the National Science Foundation under Award Number 2112880.
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Rudelius, T. Revisiting the refined Distance Conjecture. J. High Energ. Phys. 2023, 130 (2023). https://doi.org/10.1007/JHEP09(2023)130
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DOI: https://doi.org/10.1007/JHEP09(2023)130