Abstract
We determine the first curvature correction for the string amplitude of two supergravity states and two Kaluza-Klein modes on AdS5×S5, which is dual to the correlator \( \left\langle {\mathcal{O}}_2{\mathcal{O}}_2{\mathcal{O}}_p{\mathcal{O}}_p\right\rangle \) of half-BPS operators in \( \mathcal{N} \) = 4 SYM theory. The result has the form of an integral over the Riemann sphere as for the usual Virasoro-Shapiro amplitude, with the insertion of single-valued multiple polylogarithms of weight three. The result fixes OPE data of single-trace operators in \( \mathcal{N} \) = 4 SYM theory at strong coupling, including operators with non-zero R-charge and odd spin. We successfully check our results by comparing to data available from integrability, localisation and consistency with a 10d effective action.
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Acknowledgments
We thank Fernando Alday, Joseph Minahan, Erik Panzer and Oliver Schnetz for useful discussions. GF thanks the Oxford Mathematical Institute for hospitality during the early stages of this work and Agnese Bissi, Parijat Dey, Simon Ekhammar and Dima Volin for valuable discussions. The work of GF is supported by Knut and Alice Wallenberg Foundation under grant KAW 2016.0129 and by VR grant 2018-04438. The work of TH is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 787185). JS is supported by the STFC grant ST/T000864/1.
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Fardelli, G., Hansen, T. & Silva, J.A. AdS Virasoro-Shapiro amplitude with KK modes. J. High Energ. Phys. 2023, 64 (2023). https://doi.org/10.1007/JHEP11(2023)064
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DOI: https://doi.org/10.1007/JHEP11(2023)064