Abstract
We study celestial amplitudes in string theory at one-loop. Celestial amplitudes describe scattering processes of boost eigenstates and relate to amplitudes in the more standard basis of momentum eigenstates through a Mellin transform. They are thus sensitive to both the ultraviolet and the infrared, which raises the question of how to appropriately take the field theory limit of string amplitudes in the celestial basis. We address this problem in the context of four-dimensional genus-one scattering processes of gluons in open string theory which reach the two-dimensional celestial sphere at null infinity. We show that the Mellin transform commutes with the adequate limit in the worldsheet moduli space and reproduces the celestial one-loop field theory amplitude expressed in the worldline formalism. The dependence on α′ continues to be a simple overall factor in one-loop celestial amplitudes albeit with a power that is shifted with respect to tree-level, thus making manifest that the dimensionless parameter \( {g}_{10}^2/{\alpha}^{\prime 3} \) organizes the loop expansion in the celestial basis. The precise way in which the amplitudes scale with this parameter depends on the number of non-compact dimensions in such a way that in 4 dimensions the scaling with α′ does agree with that at tree-level.
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Acknowledgments
L.D. is partially supported by INFN Iniziativa Specifica ST&FI. The work of F.R. has been supported by FONDECYT grants 1221920 and 1211545. H.G. is partially supported by FONDECYT grants 1230853 and 1210635. H.G. and F.R. have also been supported by ANID/ACT 210100 Anillo grant. A.P. is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 852386).
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Donnay, L., Giribet, G., González, H. et al. Celestial open strings at one-loop. J. High Energ. Phys. 2023, 47 (2023). https://doi.org/10.1007/JHEP10(2023)047
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DOI: https://doi.org/10.1007/JHEP10(2023)047