Abstract
In the Emergence Proposal in Quantum Gravity it is conjectured that all light-particle kinetic terms are absent in the fundamental ultraviolet theory and are generated by quantum corrections in the infrared. It has been argued that this may provide for some microscopic understanding of the Weak Gravity and Distance conjectures. In the present paper we take the first steps towards a systematic study of Emergence in the context of string theory. We emphasize the crucial role of the species scale in any effective field theory coupled to gravity, and discuss its computation in string theory and general systems with light towers of states. We then introduce the notion of Emergence and show how kinetic terms for moduli, gauge bosons and fermions may be generated. One-loop computations play an important role in Emergence, so we present detailed calculations in d spacetime dimensions for the wave-function renormalization of scalars, vectors and fermions. We extend and check the Emergence Proposal in a number string vacua, including 4d \( \mathcal{N} \) = 2 theories arising from type IIA on a CY3, where the towers at strong coupling are comprised by D0 and (wrapped) D2-branes, and also elaborate on how instanton corrections would fit within the emergence picture. Higher dimensional examples are also discussed, including 6d and 7d models arising from F-/M-theory on an elliptic CY3 or a K3 surface. We also consider 10d string theories and study in some detail the emergence mechanism in type IIA. We show as well how the flux potential in 4d may be obtained from the emergence prescription, by analyzing the corresponding decompactification limits to M-theory. We find that the required kinetic terms for the dual 3-form fields can arise upon integrating out towers of massive gravitini (and bosonic superpartners). Our analysis renders support to the Emergence Proposal, and to the idea that infinite distance singularities may arise in Quantum Gravity as an intrinsic infrared phenomenon.
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Acknowledgments
We would like to thank G. Bossard, J. Calderón-Infante, M. Delgado, J. Donoghe, N. Gendler, M. Graña, D. van de Heisteeg, N. Kovensky, W. Lerche, F. Marchesano, J. Mc-Namara, L. Melotti, M. Montero, T. Ortín, E. Palti, J. Parra-Martínez, A. Uranga, C. Vafa, I. Valenzuela and M. Wiesner for useful discussions and correspondence. A.C. would like to thank the Institut de Physique Théorique CEA/Saclay, as well as the Simons Center for Geometry and Physics, Stony Brook University for hospitality and support during the last stages of this work. This work is supported through the grants CEX2020-001007-S, PGC2018-095976-B-C21 and PID2019-108892RB-I00, funded by MCIN/AEI/10.13039/501100011033 and by ERDF A way of making Europe. 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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Castellano, A., Herráez, A. & Ibáñez, L.E. The emergence proposal in quantum gravity and the species scale. J. High Energ. Phys. 2023, 47 (2023). https://doi.org/10.1007/JHEP06(2023)047
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DOI: https://doi.org/10.1007/JHEP06(2023)047