Correlation functions, null polygonal Wilson loops, and local operators

Abstract

We consider the ratio of the correlation function of n+1 local operators over the correlator of the first n of these operators in planar N=4 super-Yang-Mills theory, and consider the limit where the first n operators become pairwise null separated. By studying the problem in twistor space, we prove that this is equivalent to the correlator of a n-cusp null polygonal Wilson loop with the remaining operator in general position, normalized by the expectation value of the Wilson loop itself, as recently conjectured by Alday, Buchbinder and Tseytlin. Twistor methods also provide a BCFW-like recursion relation for such correlators. Finally, we study the natural extension where n operators become pairwise null separated with k operators in general position. As an example, we perform an analysis of the resulting correlator for k=2 and discuss some of the difficulties associated to fixing the correlator completely in the strong coupling regime.

34 pages, 6 figures. v2: typos corrected and references added; v3: published version

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Cited by in corpus (17)

• Composite Operators in the Twistor Formulation of $\mathcal{N}=4$ SYM Theory
• Twistor methods for AdS${}_5$
• Correlation functions of local composite operators from generalized unitarity
• Correlation function of circular Wilson loop with two local operators and conformal invariance
• Perturbative correlation functions of null Wilson loops and local operators
• Twistor actions for gauge theory and gravity
• The 4d/2d correspondence in twistor space and holomorphic Wilson lines
• Higher loop mixed correlators in N=4 SYM
• Integrated negative geometries in ABJM
• Demystifying the twistor construction of composite operators in N=4 super-Yang-Mills theory
• Correlation functions of the chiral stress-tensor multiplet in N=4 SYM
• Semiclassical correlation functions of Wilson loops and local vertex operators
• Twistor fishnets
• Space-time CFTs from the Riemann sphere
• Lagrangian Insertion in the Light-Like Limit and the Super-Correlators/Super-Amplitudes Duality
• Holographic correlation functions of hexagon Wilson loops with one local operator
• Lectures on twistor theory