AdS Virasoro-Shapiro from dispersive sum rules

Abstract

We consider the four-point correlator of the stress-energy tensor in $\mathcal{N}=4$ SYM, to leading order in inverse powers of the central charge, but including all order corrections in $1/\lambda$. This corresponds to the AdS version of the Virasoro-Shapiro amplitude to all orders in the small ${\alpha }^{\prime }$/low energy expansion. Using dispersion relations in Mellin space, we derive an infinite set of sum rules. These sum rules strongly constrain the form of the amplitude, and determine all coefficients in the low energy expansion in terms of the CFT data for heavy string operators, in principle available from integrability. For the first set of corrections to the flat space amplitude we find a unique solution consistent with the results from integrability and localisation.

32 pages. Published version

References in corpus (12)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Holography from Conformal Field Theory
• Writing CFT correlation functions as AdS scattering amplitudes
• Comments on operators with large spin
• Sharp Boundaries for the Swampland
• Loop Corrections to Supergravity on $Ad{S}_5\times S^5$
• Dispersive CFT Sum Rules
• AdS Bulk Locality from Sharp CFT Bounds
• Four point function of $\mathcal{N}=4$ stress-tensor multiplet at strong coupling
• Applications of dispersive sum rules: $\epsilon$-expansion and holography
• Towards the Virasoro-Shapiro Amplitude in AdS5xS5
• Superconformal Invariants or How to Relate Four-point AdS Amplitudes

Cited by in corpus (19)

• The AdS Virasoro-Shapiro Amplitude
• AdS Virasoro-Shapiro from single-valued periods
• Bootstrapping $\mathcal{N}=4$ sYM correlators using integrability
• Bootstrapping 4d $\mathcal{N}=2$ gauge theories: the case of SQCD
• Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM
• Laplace-difference equation for integrated correlators of operators with general charges in $\mathcal{N}=4$ SYM
• The AdS Veneziano amplitude at small curvature
• High Energy String Scattering in AdS
• The type IIA Virasoro-Shapiro amplitude in AdS${}_4$ $\times$ CP${}^3$ from ABJM theory
• On the spectrum and structure constants of short operators in N=4 SYM at strong coupling
• Locality and Analyticity of the Crossing Symmetric Dispersion Relation
• Bootstrapping Witten diagrams via differential representation in Mellin space
• Positivity of the Hypergeometric Coon Amplitude
• 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
• FiniteFieldSolve: Exactly Solving Large Linear Systems in High-Energy Theory
• Coon unitarity via partial waves or: how I learned to stop worrying and love the harmonic numbers
• A Celestial Route to AdS Bulk Locality
• Twisted de Rham theory for string double copy in AdS