Three-loop five-leg amplitude in planar N=4 sYM near mass shell is computed via 6D unitarity cuts and dimensional reduction, confirming IR exponentiation governed by octagon anomalous dimension with each of three kinematic structures having its own function of 't Hooft coupling.
Hexagonalization of Correlation Functions
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abstract
We propose a nonperturbative framework to study general correlation functions of single-trace operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at large $N$. The basic strategy is to decompose them into fundamental building blocks called the hexagon form factors, which were introduced earlier to study structure constants using integrability. The decomposition is akin to a triangulation of a Riemann surface, and we thus call it hexagonalization. We propose a set of rules to glue the hexagons together based on symmetry, which naturally incorporate the dependence on the conformal and the R-symmetry cross ratios. Our method is conceptually different from the conventional operator product expansion and automatically takes into account multi-trace operators exchanged in OPE channels. To illustrate the idea in simple set-ups, we compute four-point functions of BPS operators of arbitrary lengths and correlation functions of one Konishi operator and three short BPS operators, all at one loop. In all cases, the results are in perfect agreement with the perturbative data. We also suggest that our method can be a useful tool to study conformal integrals, and show it explicitly for the case of ladder integrals.
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Conjecture that the three-point structure constant of one single-trace and two determinant operators in N=4 SYM is given by glued hexagon form factors, reducing to partition sums with reflections at weak coupling and matching explicit tree-level computations.
A basis of six uniform-transcendental five-point off-shell conformal integrals is constructed and mapped to known families, yielding symbol-level two-loop results for half-BPS correlators.
In the classical strong-coupling regime, half-BPS correlation functions in planar N=4 SYM exponentiate under the hexagon formalism and are governed by TBA equations structurally equivalent to Gaiotto-Moore-Neitzke equations, enabling a chi-system for both polygonal and closed geometries.
citing papers explorer
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Five legs @ three loops: N=4 sYM amplitude near mass-shell
Three-loop five-leg amplitude in planar N=4 sYM near mass shell is computed via 6D unitarity cuts and dimensional reduction, confirming IR exponentiation governed by octagon anomalous dimension with each of three kinematic structures having its own function of 't Hooft coupling.
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Structure Constants of a Single Trace Operator and Determinant Operators from Hexagon
Conjecture that the three-point structure constant of one single-trace and two determinant operators in N=4 SYM is given by glued hexagon form factors, reducing to partition sums with reflections at weak coupling and matching explicit tree-level computations.
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Notes on off-shell conformal integrals and correlation functions at five points
A basis of six uniform-transcendental five-point off-shell conformal integrals is constructed and mapped to known families, yielding symbol-level two-loop results for half-BPS correlators.
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Classical correlation functions at strong coupling from hexagonalization
In the classical strong-coupling regime, half-BPS correlation functions in planar N=4 SYM exponentiate under the hexagon formalism and are governed by TBA equations structurally equivalent to Gaiotto-Moore-Neitzke equations, enabling a chi-system for both polygonal and closed geometries.