Higher-multiplicity consistency of IST amplitudes

Determine whether the harmonic truncation that defines the four-point infinite-spin-tower amplitudes extends consistently to higher-point amplitudes, where multiple zeta values occur, while satisfying the algebraic relations among those values and amplitude factorization.

Background

The paper identifies a family of infinite-spin-tower (IST) amplitudes that satisfies the nonlinear six-point supersymmetry constraints studied on the gravitational branch of four-dimensional $\mathcal N=4$ Einstein–Yang–Mills theory. Their four-point Wilson coefficients are obtained from the heterotic-string coefficients by replacing odd zeta values with generalized harmonic numbers truncated at a finite number of massive levels.

At four points, the nonlinear constraints leave the coefficients associated with odd-zeta structures free, which permits IST solutions in addition to the heterotic-string solution. The unresolved issue is whether this truncated harmonic-number structure can be extended beyond four points, where multiple zeta values arise and must obey nontrivial algebraic identities. A consistent extension would also have to satisfy factorization, providing a possible route to constructing consistent $n$-point IST amplitudes.