The Virasoro-Shapiro amplitude in AdS5 × S5 and level splitting of 10d conformal symmetry

• Published in: The journal of high energy physics 2021-11, Vol.2021 (11), p.1-64, Article 109
• Main Authors: Aprile, F., Drummond, J. M., Paul, H., Santagata, M.
• Format: Article
• Language: English
• Subjects: 1/N Expansion; AdS-CFT Correspondence; Algorithms; Amplitudes; Classical and Quantum Gravitation; Elementary Particles; Exchanging; High energy physics; Operators; Physics; Physics and Astronomy; Polynomials; Quantum Field Theories; Quantum Field Theory; Quantum numbers; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering Amplitudes; String Theory; Supergravity; Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP11(2021)109

A bstract The genus zero contribution to the four-point correlator O p 1 O p 2 O p 3 O p 4 of half-BPS single-particle operators O p in N = 4 super Yang-Mills, at strong coupling, computes the Virasoro-Shapiro amplitude of closed superstrings in AdS 5 × S 5 . Combining Mellin space techniques, the large p limit, and data about the spectrum of two-particle operators at tree level in supergravity, we design a bootstrap algorithm which heavily constrains its α ′ expansion. We use crossing symmetry, polynomiality in the Mellin variables and the large p limit to stratify the Virasoro-Shapiro amplitude away from the ten-dimensional flat space limit. Then we analyse the spectrum of exchanged two-particle operators at fixed order in the α ′ expansion. We impose that the ten-dimensional spin of the spectrum visible at that order is bounded above in the same way as in the flat space amplitude. This constraint determines the Virasoro-Shapiro amplitude in AdS 5 × S 5 up to a small number of ambiguities at each order. We compute it explicitly for ( α′ ) 5,6,7,8,9 . As the order of α′ grows, the ten dimensional spin grows, and the set of visible two-particle operators opens up. Operators illuminated for the first time receive a string correction to their anomalous dimensions which is uniquely determined and lifts the residual degeneracy of tree level supergravity, due to ten-dimensional conformal symmetry. We encode the lifting of the residual degeneracy in a characteristic polynomial. This object carries information about all orders in α′ . It is analytic in the quantum numbers, symmetric under an AdS 5 ↔ S 5 exchange, and it enjoys intriguing properties, which we explain and detail in various cases.