The Virasoro-Shapiro amplitude in AdS${}_5\times$S${}^5$ and level splitting of 10d conformal symmetry

Abstract

The genus zero contribution to the four-point correlator $⟨{\mathcal{O}}_{p_1}{\mathcal{O}}_{p_2}{\mathcal{O}}_{p_3}{\mathcal{O}}_{p_4}⟩$ of half-BPS single-particle operators ${\mathcal{O}}_p$ in $\mathcal{N}=4$ super Yang-Mills at strong coupling computes the Virasoro-Shapiro amplitude of closed superstrings on $Ad{S}_5\times S^5$. 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 ${\alpha }^{\prime }$ 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 ${\alpha }^{\prime }$ 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 $Ad{S}_5\times S^5$ up to a small number of ambiguities at each order and we compute it explicitly for $({\alpha }^{\prime }{)}^{5,6,7,8,9}$. As the order of ${\alpha }^{\prime }$ 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. This correction 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 ${\alpha }^{\prime }$.It is analytic in the quantum numbers, symmetric under an $Ad{S}_5\leftrightarrow S^5$ exchange, and it enjoys intriguing properties, which we explain and detail in various cases.

46 pages plus Appendices A and B; v2: 48 pages plus Appendices A and B, typos fixed, match with JHEP version; v3: added funding acknowledgement

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Cited by in corpus (16)

• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• The AdS Virasoro-Shapiro Amplitude
• Ten dimensional symmetry of N=4 SYM correlators
• Cosmological Scattering Equations
• Harnessing S-Duality in $\mathcal{N}=4$ SYM & Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• BCJ relations in ${AdS}_5\times S^3$ and the double-trace spectrum of super gluons
• Laplace-difference equation for integrated correlators of operators with general charges in $\mathcal{N}=4$ SYM
• Two-particle spectrum of tensor multiplets coupled to $Ad{S}_3\times S^3$ gravity
• Higher-Dimensional Symmetry of AdS${}_2\times$S${}^2$ Correlators
• Bootstrapping Witten diagrams via differential representation in Mellin space
• The Kaluza-Klein AdS Virasoro-Shapiro Amplitude near Flat Space
• One-loop string amplitudes in AdS${}_5\times$S${}^5$: Mellin space and sphere splitting
• All Next-to-Next-to-Extremal One-Loop Correlators of AdS Supergluons and Supergravitons
• Bootstrapping AdS${}_2\times$ S${}^2$ hypermultiplets: hidden four-dimensional conformal symmetry
• Bootstrap AdS Veneziano Amplitude with Arbitrary Kaluza-Klein Modes