- Open Access
Mellin Bootstrap, Hidden 10D Symmetry and Five-Point Kaluza-Klein Functions in Supersymmetric Yang-Mills Theory
Phys. Rev. Lett. 136, 081602 – Published 26 February, 2026
DOI: https://doi.org/10.1103/3qyd-n621
Abstract
We propose an factorization formula at the level of the generating function for correlators with arbitrary Kaluza-Klein configurations and implement it in the supergravity limit of supersymmetric Yang-Mills theory. By incorporating this mechanism into Mellin space bootstrap, together with an observed symmetry under , we manage to simultaneously work out unified formulas both for all five-point half-BPS correlators and for all four-point correlators with one superdescendant. This bootstrap method is directly applicable to generic multipoint computation at tree level.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (66)
- L. Rastelli and X. Zhou, Mellin amplitudes for , Phys. Rev. Lett. 118, 091602 (2017).
- L. Rastelli and X. Zhou, How to succeed at holographic correlators without really trying, J. High Energy Phys. 04 (2017) 014.
- F. Aprile, J. M. Drummond, P. Heslop, and H. Paul, Unmixing supergravity, J. High Energy Phys. 02 (2017) 133.
- L. F. Alday and A. Bissi, Loop corrections to supergravity on , Phys. Rev. Lett. 119, 171601 (2017).
- L. F. Alday and S. Caron-Huot, Gravitational S-matrix from CFT dispersion relations, J. High Energy Phys. 12 (2017) 017.
- F. Aprile, J. M. Drummond, P. Heslop, and H. Paul, Quantum gravity from conformal field theory, J. High Energy Phys. 01 (2017) 035.
- F. Aprile, J. M. Drummond, P. Heslop, and H. Paul, Loop corrections for Kaluza-Klein AdS amplitudes, J. High Energy Phys. 05 (2017) 056.
- L. F. Alday and X. Zhou, Simplicity of AdS supergravity at one loop, J. High Energy Phys. 09 (2019) 008.
- Z. Huang and E. Y. Yuan, Graviton scattering in at two loops, J. High Energy Phys. 04 (2021) 064.
- J. M. Drummond and H. Paul, Two-loop supergravity on from CFT, J. High Energy Phys. 08 (2022) 275.
- Z. Huang, B. Wang, and E. Y. Yuan, All next-next-to-extremal one-loop correlators of AdS supergluons and supergravitons, Phys. Rev. Lett. 134, 051601 (2025).
- V. Gonçalves, Four point function of stress-tensor multiplet at strong coupling, J. High Energy Phys. 04 (2014) 150.
- L. F. Alday, A. Bissi, and E. Perlmutter, Genus-one string amplitudes from conformal field theory, J. High Energy Phys. 06 (2018) 010.
- L. F. Alday, On genus-one string amplitudes on , J. High Energy Phys. 04 (2018) 005.
- J. M. Drummond, D. Nandan, H. Paul, and K. S. Rigatos, String corrections to AdS amplitudes and the double-trace spectrum of SYM, J. High Energy Phys. 12 (2019) 173.
- J. M. Drummond and H. Paul, One-loop string corrections to AdS amplitudes from CFT, J. High Energy Phys. 03 (2019) 038.
- J. M. Drummond, H. Paul, and M. Santagata, Bootstrapping string theory on , Phys. Rev. D 108, 026020 (2023).
- J. M. Drummond, R. Glew, and H. Paul, One-loop string corrections for AdS Kaluza-Klein amplitudes, J. High Energy Phys. 12 (2020) 072.
- F. Aprile, J. M. Drummond, H. Paul, and M. Santagata, The Virasoro-Shapiro amplitude in and level splitting of 10D conformal symmetry, J. High Energy Phys. 11 (2020) 109.
- F. Aprile, J. M. Drummond, R. Glew, and M. Santagata, One-loop string amplitudes in : Mellin space and sphere splitting, J. High Energy Phys. 02 (2022) 087.
- A. Bissi, A. Sinha, and X. Zhou, Selected topics in analytic conformal bootstrap: A guided journey, Phys. Rep. 991, 1 (2022).
- P. Heslop, The SAGEX review on scattering amplitudes, chapter 8: Half BPS correlators, J. Phys. A 55, 443009 (2022).
- S. Caron-Huot and A.-K. Trinh, All tree-level correlators in supergravity: Hidden ten-dimensional conformal symmetry, J. High Energy Phys. 01 (2018) 196.
- T. Abl, P. Heslop, and A. E. Lipstein, Towards the Virasoro-Shapiro amplitude in , J. High Energy Phys. 04 (2020) 237.
- S. Caron-Huot and F. Coronado, Ten dimensional symmetry of SYM correlators, J. High Energy Phys. 03 (2021) 151.
- S. Caron-Huot, F. Coronado, and B. Mühlmann, Determinants in self-dual SYM and twistor space, J. High Energy Phys. 08 (2023) 008.
- F. Aprile and P. Vieira, Large explorations. From SUGRA to big STRINGS in Mellin space, J. High Energy Phys. 12 (2020) 206.
- Z. Huang, B. Wang, E. Y. Yuan, and J. Zhang, All Five-Point Kaluza-Klein correlators and hidden 8D symmetry in AdS5S3, Phys. Rev. Lett. 134, 161601 (2025).
- B. Wang, D. Wu, and E. Y. Yuan, The Kaluza-Klein AdS Virasoro-Shapiro amplitude near flat space, Phys. Rev. Lett. 135, 041603 (2025).
See also [31, 32] for recent studies on hidden 10D symmetry in giant graviton correlators.
- J. Chen, Y. Jiang, and X. Zhou, Giant graviton correlators as defect systems, Phys. Rev. Lett. 135, 081602 (2025).
- Y. Wu, Y. Jiang, C. Liu, and Y. Zhang, All giant graviton two-point functions at two-loops, arXiv:2509.23161.
- L. F. Alday, V. Gonçalves, and X. Zhou, Supersymmetric five-point gluon amplitudes in AdS space, Phys. Rev. Lett. 128, 161601 (2022).
- L. F. Alday, V. Gonçalves, M. Nocchi, and X. Zhou, Six-point AdS gluon amplitudes from flat space and factorization, Phys. Rev. Res. 6, L012041 (2024).
- Q. Cao, S. He, and Y. Tang, Constructibility of AdS supergluon amplitudes, Phys. Rev. Lett. 133, 021605 (2024).
- Q. Cao, S. He, X. Li, and Y. Tang, Supergluon scattering in AdS: Constructibility, spinning amplitudes, and new structures, J. High Energy Phys. 10 (2024) 040.
- V. Gonçalves, R. Pereira, and X. Zhou, five-point function from supergravity, J. High Energy Phys. 10 (2019) 247.
- V. Gonçalves, C. Meneghelli, R. Pereira, J. Vilas Boas, and X. Zhou, Kaluza-Klein five-point functions from supergravity, J. High Energy Phys. 08 (2023) 067.
- V. Goncalves, M. Nocchi, and X. Zhou, Dissecting supergraviton six-point function with lightcone limits and chiral algebra, J. High Energy Phys. 06 (2025) 173.
- N. Drukker and J. Plefka, Superprotected n-point correlation functions of local operators in super Yang-Mills, J. High Energy Phys. 04 (2009) 052.
- M. S. Costa, J. Penedones, D. Poland, and S. Rychkov, Spinning conformal correlators, J. High Energy Phys. 11 (2011) 071.
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/3qyd-n621 for details on the Mellin formalism [including the derivation of (25) and (44)] and superspace methods. Supplemental Material includes Refs. [22,41,43–46].
- V. Gonçalves, J. Penedones, and E. Trevisani, Factorization of Mellin amplitudes, J. High Energy Phys. 10 (2014) 040.
- S. Weinberg, Six-dimensional methods for four-dimensional conformal field theories, Phys. Rev. D 82, 045031 (2010).
- D. Simmons-Duffin, Projectors, shadows, and conformal blocks, J. High Energy Phys. 04 (2012) 146.
- M. S. Costa, T. Hansen, J. Penedones, and E. Trevisani, Projectors and seed conformal blocks for traceless mixed-symmetry tensors, J. High Energy Phys. 07 (2016) 018.
Because of the factors, the sum is automatically truncated to a finite number of integer points such that all .
- F. A. Dolan, L. Gallot, and E. Sokatchev, On four-point functions of -BPS operators in general dimensions, J. High Energy Phys. 09 (2004) 056.
At tree level, multitrace exchanges are encoded in poles of functions in the conventional Mellin transformation.
- A. L. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju, and B. C. van Rees, A natural language for AdS/CFT correlators, J. High Energy Phys. 11 (2011) 095.
When restricted to the reduced correlators, this symmetry can be viewed as an element in the hidden 10D conformal group.
The same symmetry was discovered in [19] for stringy corrections. We thank Francesco Aprile and Michele Santagata for pointing this out.
The amplitude might appear to violate the symmetry , but in this three-point amplitude we have .
We will see that, after the bootstrap computation, the result can indeed be put in a factorized form with superconformal invariants and reduced amplitudes depending only on .
In fact, we did not write down an ansatz for and explicitly in the actual bootstrap computation. All constraints on these polynomials should be understood as imposed directly on the rhs of (39) and (40).
- N. Ceplak, S. Giusto, M. R. R. Hughes, and R. Russo, Holographic correlators with multi-particle states, J. High Energy Phys. 09 (2021) 204.
- W.-J. Ma and X. Zhou, Scattering bound states in AdS, J. High Energy Phys. 08 (2022) 107.
- G. Fardelli, A. L. Fitzpatrick, and W. Li, Holography and Regge phases with U(1) charge, J. High Energy Phys. 08 (2024) 202.
- F. Aprile, S. Giusto, and R. Russo, Holographic correlators with BPS bound states in SYM, Phys. Rev. Lett. 134, 091602 (2025).
- P. Kravchuk and J. A. Mann, AdS -body problem at large spin, J. High Energy Phys. 10 (2025) 004.
- A. Bissi, G. Fardelli, and A. Manenti, Composite operators in Super Yang-Mills, J. High Energy Phys. 07 (2024) 074.
- F. Aprile, S. Giusto, and R. Russo, Four-point correlators with BPS bound states in and , J. High Energy Phys. 08 (2025) 193.
- J. Vilas Boas, five-point function of SYM and stringy corrections, arXiv:2507.12533.
- T. Bargheer, T. Fleury, and V. Gonçalves, Higher-point integrands in super Yang-Mills theory, SciPost Phys. 15, 059 (2023).
- T. Bargheer, A. Bekov, C. Bercini, and F. Coronado, Higher-point correlators in SYM: Generating functions, arXiv:2509.14332.
- X. Zhou, Double copy relation in AdS space, Phys. Rev. Lett. 127, 141601 (2021).