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.

arXiv comment46 pages plus Appendices A and B; v2: 48 pages plus Appendices A and B, typos fixed, match with JHEP version; v3: added funding acknowledgement

References in corpus (39)

• Review of AdS/CFT Integrability: An Overview
• Holography from Conformal Field Theory
• Writing CFT correlation functions as AdS scattering amplitudes
• Mellin amplitudes for $Ad{S}_5\times S^5$
• How to Succeed at Holographic Correlators Without Really Trying
• Gravitational S-matrix from CFT dispersion relations
• Loop Corrections to Supergravity on $Ad{S}_5\times S^5$
• $\mathcal{N}=4$ Super-Yang-Mills Correlators at Strong Coupling from String Theory and Localization
• Partial non-renormalisation of the stress-tensor four-point function in N=4 SYM and AdS/CFT
• Low energy expansion of the four-particle genus-one amplitude in type II superstring theory
• All Tree-Level Correlators in AdS${}_5\times$S${}_5$ Supergravity: Hidden Ten-Dimensional Conformal Symmetry
• Quantum Gravity from Conformal Field Theory
• $20^{\prime }$ Five-Point Function from $Ad{S}_5\times S^5$ Supergravity
• Unmixing Supergravity
• Conformal Partial Wave Expansions for N=4 Chiral Four Point Functions
• Genus-One String Amplitudes from Conformal Field Theory
• Far Beyond the Planar Limit in Strongly-Coupled $\mathcal{N}=4$ SYM
• Four point function of $\mathcal{N}=4$ stress-tensor multiplet at strong coupling
• The double-trace spectrum of N=4 SYM at strong coupling
• Loop corrections for Kaluza-Klein AdS amplitudes
• Genus-2 Holographic Correlator on $Ad{S}_5\times S^5$ from Localization
• $\mathbf{Ad}{\mathbf{S}}_3\times {\mathbf{S}}^3$ Tree-Level Correlators: Hidden Six-Dimensional Conformal Symmetry
• New Modular Invariants in $\mathcal{N}=4$ Super-Yang-Mills Theory
• One-loop amplitudes in $Ad{S}_5\times S^5$ supergravity from $\mathcal{N}=4$ SYM at strong coupling
• Perturbative Four-Point Functions In Planar N=4 SYM From Hexagonalization
• Exact null octagon
• Octagon at finite coupling
• Large $p$ explorations. From SUGRA to big STRINGS in Mellin space
• Holographic correlators in AdS${}_3$ without Witten diagrams
• The CFT${}_6$ origin of all tree-level 4-point correlators in AdS${}_3\times S^3$
• Single Particle Operators and their Correlators in Free $\mathcal{N}=4$ SYM
• String corrections to AdS amplitudes and the double-trace spectrum of N=4 SYM
• Towards the Virasoro-Shapiro Amplitude in AdS5xS5
• One-loop string corrections to AdS amplitudes from CFT
• Harmonic Superspace from the $Ad{S}_5\times S^5$ Pure Spinor Formalism
• Towards All Loop Supergravity Amplitudes on $Ad{S}_5\times S^5$
• On Genus-one String Amplitudes on $Ad{S}_5\times S^5$
• One-loop string corrections for AdS Kaluza-Klein amplitudes
• Open-closed superstring amplitudes using vertex operators in ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$

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• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
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• Cosmological Scattering Equations
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• 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