Superprotected n-point correlation functions of local operators in N=4 super Yang-Mills

Abstract

In this paper we study the n-point correlation functions of two different families of local gauge invariant operators in N=4 supersymmetric Yang-Mills theory. The main idea is to consider the correlation functions of operators which all share a number of supersymmetries irrespective of their relative locations. We achieve this by equipping the operators with explicit space-time dependence. We provide evidence by different methods that these n-point correlators do not receive quantum corrections in perturbation theory and are hence given exactly by their tree-level result. The arguments rely on explicit checks for general four-point correlators, some five-point and six-point correlators and a more abstract calculation based on a novel topological twisting of N=4 supersymmetric Yang-Mills theory.

38 pages, half of them appendices; v2 typos corrected

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• Bootstrapping the half-BPS line defect
• Tessellating cushions: four-point functions in N=4 SYM
• Correlators of local operators and 1/8 BPS Wilson loops on S^2 from 2d YM and matrix models
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS
• Exact Three-Point Functions of Determinant Operators in Planar N=4 Supersymmetric Yang-Mills Theory
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• Operator Mixing in Large $N$ Superconformal Field Theories on ${\mathbb{S}}^4$ and Correlators with Wilson loops
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS${}_7\times$S${}^4$
• Correlators of supersymmetric Wilson-loops, protected operators and matrix models in N=4 SYM
• Broken global symmetries and defect conformal manifolds
• Bremsstrahlung function, leading Luscher correction at weak coupling and localization
• Exact Correlators on the Wilson Loop in $\mathcal{N}=4$ SYM: Localization, Defect CFT, and Integrability
• Supersymmetric Wilson loops in N=4 SYM and pure spinors
• Multipoint correlators on the supersymmetric Wilson line defect CFT
• Correlators of chiral primaries and 1/8 BPS Wilson loops from perturbation theory
• Decagon at Two Loops
• Observations on BPS observables in 6d
• Higher-Point Integrands in N=4 super Yang-Mills Theory
• On three-point functions in ABJM and the latitude Wilson loop
• Fermionic Bogomolnyi-Prasad-Sommerfield Wilson loops in four-dimensional $\mathcal{N}=2$ superconformal gauge theories
• The four-point function of determinant operators in $\mathcal{N}=4$ SYM
• D-branes and Orbit Average
• Three-point Functions in $\mathcal{N}=4$ SYM at Finite $N_c$ and Background Independence
• Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators
• Higher-Point Correlators in N=4 SYM: Generating Functions
• Three-point Functions in Aharony--Bergman--Jafferis--Maldacena Theory and Integrable Boundary States
• Three-Point Functions in ABJM and Bethe Ansatz
• Two-Point Correlator of Chiral Primary Operators with a Wilson Line Defect in $\mathcal{N}=4$ SYM
• Rebooting quarter-BPS operators in $\mathcal{N}=4$ Super Yang-Mills
• Generating functions for Higgs/Coulomb branch operators from 1d-3d cohomological equivalence