Researchers resummed the back-to-back energy-energy correlator plateau from weak to strong coupling and completed the N3LL calculation with an agentic workflow

In N=4 supersymmetric Yang-Mills theory, the leading- and next-to-leading-power logarithms of the back-to-back energy-energy correlator are resummed through N3LL accuracy, including non-planar contributions. Independent finite-coupling information from integrability was already available for the twist-two leading-power sector, while extending the next-to-leading-power logarithms to high logarithmic accuracy required extensive symbolic computation; this work provides the next-to-leading-power function, which contains an error function generated by the all-order logarithmic sum. The derivation uses large-spin methods, crossing symmetry, and Mellin projection, with inputs being the twist-two anomalous dimension, the corresponding OPE coefficients, and fixed-order EEC results; the text states that the remaining terms are in exact agreement with the leading- and next-to-leading-power coefficient predictions from twist conformal block resummation, providing an independent check.

The next-to-leading-power terms change both the plateau height and the manner in which the plateau approaches the endpoint. The leading-power result alone does not determine the full endpoint, so the authors define the endpoint plateau height as a function of coupling, containing additional endpoint information not captured by the twist-two leading-power contribution; the next-to-leading-power resummation provides a weak-coupling approximation for this residual contribution. The text reports that the next-to-leading-power function contains terms proportional to specific structures together with a term independent of coupling, and that as the coupling goes to zero the relevant terms vanish, leaving a finite next-to-leading-power correction; Figure 1 shows the result with the LL through N3LL towers.

The authors construct an asymptotically constrained interpolation connecting the weak-coupling endpoint, finite-coupling bootstrap information, and the strong-coupling result, and it fits the finite-coupling bootstrap data well. The weak-coupling plateau height has an essential singularity at zero coupling that does not admit a weak-coupling power expansion, while the strong-coupling endpoint approaches the supergravity prediction with stringy corrections; by construction the interpolation reproduces the leading non-analytic Sudakov behavior at weak coupling and matches the supergravity result with its leading correction at strong coupling. The interpolation form is constrained by the weak- and strong-coupling asymptotics and is compared with finite-coupling bootstrap data in Figure 3; the authors describe it as a compact interpolation of the available all-coupling information rather than a first-principles determination.

The calculation was implemented with a human-in-the-loop agentic workflow, and an audit and independent test show that agents perform many local calculations reliably but still require substantial intervention from human experts in long-horizon calculations. The authors carried out the N3LL EEC calculation with GPT-5.5 in a human-in-the-loop workflow and tested seven models on fifteen individual steps without human feedback; each benchmark task starts independently from validated upstream input, so errors do not propagate between tasks. The text reports different correct-output rates for the first four steps versus Steps 5-15, notes that none of the seven models completed the large-spin expansion in Step 6 or the final fixed-order EEC comparison in Step 15, and that no model passed all fifteen tasks; in Step 5 GPT-5.5 chose an insufficient expansion depth, and the omissions propagated through crossing and Mellin projection to produce incorrect endpoint coefficients, which human experts corrected by working backward from the final N3LL coefficients.

The result applies to the back-to-back EEC endpoint in N=4 supersymmetric Yang-Mills theory within the conformal-collider setup, where the coupling can be varied without introducing a mass scale. The weak-coupling resummation becomes increasingly accurate as the coupling decreases, while the strong-coupling string description provides an accurate description from parametrically large coupling down to intermediate coupling, leaving a finite intermediate-coupling window between them. The interpolation provides a prediction for this crossover region and can be further tested by planar bootstrap constraints at intermediate coupling. For a broader readership, this offers a framework in which perturbative resummation, conformal bootstrap, and stringy corrections are compared on a single endpoint quantity.

The coupling dependence of the full plateau remains to be determined from first principles, and the next-to-leading-power logarithms computed here do not fix the full coupling dependence of the residual endpoint contribution. The nonperturbative structure of the intermediate-coupling window remains to be understood, and sharper planar bootstrap bounds could test the interpolation. Which features of the next-to-leading-power resummation persist in QCD remains an open question, since there the coupling runs and hadronization becomes important at low scales. In addition, several equations and table entries in the loaded text appear as placeholders, so the specific numerical values in Figures 2, 3, and 4 and Table 1 cannot be read from the text; quantitative statements about the interpolation fit quality and per-model step pass rates therefore rest on the prose alone.