A non-renormalization theorem for chiral primary 3-point functions

Abstract

In this note we prove a non-renormalization theorem for the 3-point functions of 1/2 BPS primaries in the four-dimensional N = 4 SYM and chiral primaries in two dimensional N =(4,4) SCFTs. Our proof is rather elementary: it is based on Ward identities and the structure of the short multiplets of the superconformal algebra and it does not rely on superspace techniques. We also discuss some possible generalizations to less supersymmetric multiplets.

32 pages, added references, corrected typos

References in corpus (21)

• Gauge Theory Correlators from Non-Critical String Theory
• Microscopic Origin of the Bekenstein-Hawking Entropy
• An Index for 4 dimensional Super Conformal Theories
• Black Hole Entropy in M-Theory
• Counting chiral primaries in N=1 d=4 superconformal field theories
• On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
• Bonus Symmetries of N=4 Super-Yang-Mills Correlation Functions via AdS Duality
• A non-renormalization theorem for conformal anomalies
• Nilpotent invariants in N=4 SYM
• Bonus Symmetry and the Operator Product Expansion of N=4 Super-Yang-Mills
• Worldsheet correlators in AdS(3)/CFT(2)
• Topological Anti-Topological Fusion in Four-Dimensional Superconformal Field Theories
• Connections on the State-Space over Conformal Field Theories
• Matching of correlators in AdS_3/CFT_2
• Explicit construction of nilpotent covariants in N=4 SYM
• OPEs and 3-point correlators of protected operators in N=4 SYM
• The chiral ring of AdS3/CFT2 and the attractor mechanism
• Exact N=4 correlators of AdS(3)/CFT(2)
• Worldsheet four-point functions in AdS(3)/CFT(2)
• Some Systematics of the Coupling Constant Dependence of N=4 Yang-Mills
• Worldsheet operator product expansions and p-point functions in AdS3/CFT2

Cited by in corpus (77)

• Infinite Chiral Symmetry in Four Dimensions
• Mellin amplitudes for $Ad{S}_5\times S^5$
• How to Succeed at Holographic Correlators Without Really Trying
• Habemus Superstratum! A constructive proof of the existence of superstrata
• W Symmetry in six dimensions
• $\mathcal{N}=4$ Super-Yang-Mills Correlators at Strong Coupling from String Theory and Localization
• Correlation Functions of Coulomb Branch Operators
• The $\mathcal{N}=2$ superconformal bootstrap
• $20^{\prime }$ Five-Point Function from $Ad{S}_5\times S^5$ Supergravity
• Asymptotically-flat supergravity solutions deep inside the black-hole regime
• A holographic dual for string theory on ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$
• $t{t}^{\ast }$ equations, localization and exact chiral rings in 4d N=2 SCFTs
• $\mathbf{Ad}{\mathbf{S}}_3\times {\mathbf{S}}^3$ Tree-Level Correlators: Hidden Six-Dimensional Conformal Symmetry
• On exact correlation functions in SU(N) $\mathcal{N}=2$ superconformal QCD
• Exact correlation functions in SU(2) N=2 superconformal QCD
• Supercharging Superstrata
• Protected string spectrum in AdS3/CFT2 from worldsheet integrability
• Correlators of the symmetric product orbifold
• Operator Mixing in Large $N$ Superconformal Field Theories on ${\mathbb{S}}^4$ and Correlators with Wilson loops
• Superconformal surfaces in four dimensions
• Large N Correlation Functions in Superconformal Field Theories
• Unitary 4-point correlators from classical geometries
• M-theory Superstrata and the MSW String
• Large-N correlation functions in $\mathcal{N}=2$ superconformal QCD
• Operator mixing for string states in the D1-D5 CFT near the orbifold point
• String correlators on ${\text{AdS}}_3$: Three-point functions
• (2,2) Superconformal Bootstrap in Two Dimensions
• Superstrata
• On the large R-charge $\mathcal{N}=2$ chiral correlators and the Toda equation
• Holographic 4-point correlators with heavy states
• Growing Extra Dimensions in AdS/CFT
• Extremal vs. Non-Extremal Correlators with Giant Gravitons
• AdS${}_3$ Holography at Dimension Two
• Two-point functions in AdS/dCFT and the boundary conformal bootstrap equations
• Supercharged AdS${}_3$ Holography
• Genus Two Partition Functions and Renyi Entropies of Large c CFTs
• Maximal $U(1{)}_Y$-violating $n$-point correlators in $\mathcal{N}=4$ super-Yang-Mills theory
• Absorption of closed strings by giant gravitons
• Conformal Perturbation Theory for Twisted Fields
• Non-planar data of $\mathcal{N}=4$ SYM
• Laplace-difference equation for integrated correlators of operators with general charges in $\mathcal{N}=4$ SYM
• From Schurs to Giants in ABJ(M)
• AdS${}_3$ holography for non-BPS geometries
• Geometry of Higgs-branch superconformal primary bundles
• On the Dynamics of Protected Ramond Ground States in the D1-D5 CFT
• BPS coherent states and localization
• Entanglement Entropy and D1-D5 geometries
• Three-Point Functions of Twist-Two Operators in N=4 SYM at One Loop
• Journey to the Center of the Fuzzball
• Worldsheet computation of heavy-light correlators
• Type-B Anomaly Matching and the 6D (2,0) Theory
• Integrable bootstrap for AdS3/CFT2 correlation functions
• ABJ(M) Chiral Primary Three-Point Function at Two-loops
• Dynamics of R-neutral Ramond fields in the D1-D5 SCFT
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Protected states in $\mbox{AdS}_3$ backgrounds from integrability
• Fermionic Bogomolnyi-Prasad-Sommerfield Wilson loops in four-dimensional $\mathcal{N}=2$ superconformal gauge theories
• Non-Perturbative String Theory from AdS/CFT
• Corrections in the relative entropy of black hole microstates
• $Ad{S}_5\times S^5$ supergravity vertex operators
• Thresholds of Large N Factorization in CFT4 : Exploring bulk spacetime in AdS5
• On the Kähler-Hodge structure of superconformal manifolds
• D-branes and Orbit Average
• Perturbed symmetric-product orbifold: first-order mixing and puzzles for integrability
• Conformal field theories dual to quantum gravity with strongly coupled matter
• Mellin amplitudes for $Ad{S}_3\times S^3$
• Four-point correlators in N=4 SYM from AdS${}_5$ bubbling geometries
• Structure constants of $\beta$ deformed super Yang-Mills
• Pulsating strings from two dimensional CFT on $(T^4{)}^N/S(N)$
• Hexagonalization in $Ad{S}_3\times S^3\times T^4$: Mirror Corrections
• Three-Point Functions in ABJM and Bethe Ansatz
• The Covariant Chiral Ring
• Integrability and Conformal Blocks for Surface Defects in $\mathcal{N}=4$ SYM
• Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence
• Quantum Spectral Curve for AdS${}_3$/CFT${}_2$: a proposal
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality
• Rebooting quarter-BPS operators in $\mathcal{N}=4$ Super Yang-Mills