Abstract
The Swampland Distance Conjecture (SDC) states that, as we move towards an infinite distance point in moduli space, a tower of states becomes exponentially light with the geodesic distance in any consistent theory of Quantum Gravity. Although this fact has been tested in large sets of examples, it is fair to say that a bottom-up justification based on fundamental Quantum Gravity principles that explains both the geodesic requirement and the exponential behavior has been missing so far. In the present paper we address this issue by making use of the Covariant Entropy Bound as applied to the EFT. When applied to backgrounds of the Dynamical Cobordism type in theories with a moduli space, we are able to recover these main features of the SDC. Moreover, this naturally leads to universal lower and upper bounds on the ‘decay rate’ parameter λsp of the species scale, that we propose as a convex hull condition under the name of Species Scale Distance Conjecture (SSDC). This is in contrast to already proposed universal bounds, that apply to the SDC parameter of the lightest tower. We also extend the analysis to the case in which asymptotically exponential potentials are present, finding a nice interplay with the asymptotic de Sitter conjecture. To test the SSDC, we study the convex hull that encodes the large-moduli dependence of the species scale. In this way, we show that the SSDC is the strongest bound on the species scale exponential rate which is preserved under dimensional reduction and we verify it in M-theory toroidal compactifications.
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Acknowledgments
We would like to thank G. Aldazabal, F. Marchesano, M. Montero, D. Prieto, I. Ruiz, A. Uranga, I. Valenzuela and M. Wiesner for useful discussions and correspondence. J.C. would like to thank the Instituto de Física Teórica in Madrid for hospitality during early stages of this work. A.C. would like to thank the Theoretical Physics Department at CERN for hospitality and support during the last stages of this work. This work is supported through the grants CEX2020-001007-S and PID2021-123017NB-I00, funded by MCIN/AEI/10.13039/5011 00011033 and by ERDF A way of making Europe. The work by J.C. is partially supported by the FPU grant no. FPU17/04181 from the Spanish Ministry of Education. The work of A.C. is supported by the Spanish FPI grant No. PRE2019-089790 and by the Spanish Science and Innovation Ministry through a grant for postgraduate students in the Residencia de Estudiantes del CSIC. The work of A.H. is supported by the ERC Consolidator Grant 772408-Stringlandscape.
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Calderón-Infante, J., Castellano, A., Herráez, A. et al. Entropy bounds and the species scale distance conjecture. J. High Energ. Phys. 2024, 39 (2024). https://doi.org/10.1007/JHEP01(2024)039
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DOI: https://doi.org/10.1007/JHEP01(2024)039