We construct generating functions of five- and six-point correlators up to two loops at weak 't Hooft coupling in planar N=4 SYM. These generating functions unify the correlators of the lightest scalar operator in the stress-tensor multiplet with those of all higher R-charge single-trace half-BPS scalar operators, thereby extending previous results for four-point loop integrands. At the integrated level, they are represented as sums of conformal integrals with coefficients exhibiting ten-dimensional poles that combine spacetime and R-charge distances. Our results show that higher-order poles are captured by products of lower-point generating functions. We also extract new OPE data on spinning structure constants, and compare these to integrability-based computations, finding good agreement.
Five- and six-point correlators of all single-trace half-BPS scalar operators in planar N=4 SYM admit, up to two loops at weak coupling, generating-function representations as sums of conformal integrals whose coefficients are organized by 10D poles combining spacetime and R-charge distances, with higher-order poles given by products of lower-point generating functions.
That the 10D-distance / hidden-symmetry structure known for four-point half-BPS correlators extends in a controlled, well-defined way to five- and six-point correlators at the integrated (not just integrand) level — the abstract asserts this structurally but offers no proof sketch in the abstract; the factorization of higher-order poles into lower-point generating functions is a strong structural claim whose derivation is not visible without the full text.
1/ N=4 SYM has a "hidden" 10D symmetry that organizes four-point correlators of half-BPS operators into compact generating functions whose poles encode both spacetime and R-charge separations. This paper pushes that program to five and six points at two loops. 2/ The authors claim the integrated correlators are again sums of standard conformal integrals weighted by 10D poles, and crucially that higher-order poles factorize as products of lower-point generating functions — a recursive structure if it holds. 3/ As a check, they extract spinning OPE coefficients from these correlators and compare against integrability-based predictions, reporting good agreement. The work is incremental but structurally non-trivial; verification requires reading the full construction.
Physicists found a tidy formula that packages many particle-scattering numbers together using a hidden ten-dimensional pattern.
Abstract-only review. The paper extends an established program (10D symmetry / generating functions for half-BPS correlators in planar N=4 SYM, originating in work by Caron-Huot, Coronado, and others) from four-point integrands to five- and six-point correlators at one and two loops. The claims are technically plausible and consistent with known structural results: the appearance of 10D poles unifying spacetime and R-charge distances is a documented feature of four-point correlators of half-BPS operators in N=4 SYM, and the factorization of higher-order poles into products of lower-point objects is a structural statement amenable to direct check. The OPE cross-check against integrability for spinning structure constants provides an independent (if "good agreement"-level qualitative) consistency test. Without access to the full text I cannot verify the integrand construction, the conformal integral basis, or the precise definition of the 10D distance at higher points, where the geometric origin of the 10D structure is less established than at four points. Confidence kept LOW.