Loop corrections for Kaluza-Klein AdS amplitudes

Abstract

Recently we conjectured the four-point amplitude of graviton multiplets in ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ at one loop by exploiting the operator product expansion of $\mathcal{N}=4$ super Yang-Mills theory. Here we give the first extension of those results to include Kaluza-Klein modes, obtaining the amplitude for two graviton multiplets and two states of the first KK mode. Our method again relies on resolving the large N degeneracy among a family of long double-trace operators, for which we obtain explicit formulas for the leading anomalous dimensions. Having constructed the one-loop amplitude we are able to obtain a formula for the one-loop corrections to the anomalous dimensions of all twist five double-trace operators.

37 pages. One ancillary file containing data on the correlators

References in corpus (6)

• Holography from Conformal Field Theory
• Mellin amplitudes for $Ad{S}_5\times S^5$
• Loop Corrections to Supergravity on $Ad{S}_5\times S^5$
• Anomalous dimensions of high-spin operators beyond the leading order
• Conjectures for Large N Superconformal N=4 Chiral Primary Four Point Functions
• Four-point correlators with higher weight superconformal primaries in the AdS/CFT Correspondence

Cited by in corpus (60)

• $d$-dimensional SYK, AdS Loops, and $6j$ Symbols
• $20^{\prime }$ Five-Point Function from $Ad{S}_5\times S^5$ Supergravity
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Far Beyond the Planar Limit in Strongly-Coupled $\mathcal{N}=4$ SYM
• The double-trace spectrum of N=4 SYM at strong coupling
• Genus-2 Holographic Correlator on $Ad{S}_5\times S^5$ from Localization
• Modular Invariance in Superstring Theory From $\mathcal{N}=4$ Super-Yang-Mills
• Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory
• $\mathbf{Ad}{\mathbf{S}}_3\times {\mathbf{S}}^3$ 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
• Unitarity Methods in AdS/CFT
• CFT Unitarity and the AdS Cutkosky Rules
• On Superconformal Four-Point Mellin Amplitudes in Dimension $d>2$
• Recursion Relations in Witten Diagrams and Conformal Partial Waves
• Holographic Four-Point Functions in the (2, 0) Theory
• Loops in AdS: From the Spectral Representation to Position Space
• Single Particle Operators and their Correlators in Free $\mathcal{N}=4$ SYM
• The CFT${}_6$ origin of all tree-level 4-point correlators in AdS${}_3\times S^3$
• Growing Extra Dimensions in AdS/CFT
• String corrections to AdS amplitudes and the double-trace spectrum of N=4 SYM
• One-loop Gluon Amplitudes in AdS
• Bootstrapping holographic defect correlators in $\mathcal{N}=4$ super Yang-Mills
• Towards the Virasoro-Shapiro Amplitude in AdS5xS5
• On spinning loop amplitudes in Anti-de Sitter space
• Maximal $U(1{)}_Y$-violating $n$-point correlators in $\mathcal{N}=4$ super-Yang-Mills theory
• From bulk loops to boundary large-N expansion
• All Holographic Four-Point Functions in All Maximally Supersymmetric CFTs
• The Virasoro-Shapiro amplitude in AdS${}_5\times$S${}^5$ and level splitting of 10d conformal symmetry
• ABJM at Strong Coupling from M-theory, Localization, and Lorentzian Inversion
• Modular invariant holographic correlators for $\mathcal{N}=4$ SYM with general gauge group
• Four-point functions of 1/2-BPS operators of any weights in the supergravity approximation
• One-loop string corrections to AdS amplitudes from CFT
• 6d (2,0) and M-theory at 1-loop
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• All five-loop planar four-point functions of half-BPS operators in $\mathcal{N}=4$ SYM
• Opacity from Loops in AdS
• Analytical evaluation of AdS${}_4$ Witten diagrams as flat space multi-loop Feynman integrals
• 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
• On Holography in General Background and the Boundary Effective Action from AdS to dS
• Loops in AdS: From the Spectral Representation to Position Space II
• Four-point functions of all-different-weight chiral primary operators in the supergravity approximation
• Two-particle spectrum of tensor multiplets coupled to $Ad{S}_3\times S^3$ gravity
• AdS super gluon scattering up to two loops: A position space approach
• On one loop corrections in higher spin gravity
• One-loop string corrections for AdS Kaluza-Klein amplitudes
• Recursion Relations for Anomalous Dimensions in the 6d $(2,0)$ Theory
• Notes on gravity multiplet correlators in $Ad{S}_3\times S^3$
• Bootstrapping mixed correlators in $\mathcal{N}=4$ Super Yang-Mills
• Holographic S-fold theories at one loop
• $Ad{S}_5\times S^5$ supergravity vertex operators
• The Kaluza-Klein AdS Virasoro-Shapiro Amplitude near Flat Space
• Scattering bound states in AdS
• One-loop string amplitudes in AdS${}_5\times$S${}^5$: Mellin space and sphere splitting
• Bootstrapping string theory on AdS${}_5\times S^5$
• 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
• Superconformal blocks in diverse dimensions and $BC$ symmetric functions
• Correlation functions at the bulk point singularity from the gravitational eikonal S-matrix