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

A bstract The genus zero contribution to the four-point correlator $$ \left\langle {\mathcal{O}}_{p_1}{\mathcal{O}}_{p_2}{\mathcal{O}}_{p_3}{\mathcal{O}}_{p_4}\right\rangle O p 1 2 3 4 of half-BPS single-particle operators {\mathcal{O}}_p in \mathcal{N} N = 4 super Yang-Mills, at strong coupling, computes Virasoro-Shapiro amplitude closed superstrings AdS 5 × S . Combining Mellin space techniques, large p limit, and data about spectrum two-particle tree level supergravity, we design a bootstrap algorithm which heavily constrains its α ′ expansion. We use crossing symmetry, polynomiality variables limit stratify away from ten-dimensional flat limit. Then analyse exchanged fixed order impose that spin visible is bounded above same way as amplitude. This constraint determines up small number ambiguities each order. compute it explicitly for ( α′ ) 5,6,7,8,9 As grows, ten dimensional set opens up. Operators illuminated first time receive string correction their anomalous dimensions uniquely determined lifts residual degeneracy due conformal symmetry. encode lifting characteristic polynomial. object carries information all orders It analytic quantum numbers, symmetric under an ↔ exchange, enjoys intriguing properties, explain detail various cases.