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

Abstract

The genus zero contribution to the four-point correlator 〈Op1Op2Op3Op4〉 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 AdS₅× S⁵. 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 AdS₅× S⁵ 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 AdS₅ ↔ S⁵ exchange, and it enjoys intriguing properties, which we explain and detail in various cases.

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