Underlying principle for scalar parity and weaker replacements

Determine whether the scalar-parity condition imposed on selected six-point components follows from a more general physical principle, or whether it can be replaced by a weaker condition that still yields the four-point master equations.

Background

Scalar parity is a central input in the paper’s derivation: after a collinear limit and pole subtraction, it removes the regular six-point remainder and converts factorization data into closed constraints on four-point amplitudes. The condition is imposed only on selected six-point scalar components rather than derived from a broader physical principle.

The authors explicitly leave unresolved both the conceptual origin of this scalar-parity condition and the possibility of weakening it. Resolving this issue would determine whether the resulting amplitude constraints are consequences of more fundamental principles or depend on a special component-level assumption.

References

Several questions remain open. Firstly, one should explore the constraint of maximal supersymmetry for gauge-gravity coupled system. Recent analysis has found non-linear constraints that mixes the single- and double-trace Wilson coefficients in the gluon sector, with promising numeric bounds that isolate Heterotic and IST. It will be interesting to find the exact form of identity that gives rise to these non-linear constraints. Scalar parity is imposed as a condition on selected six-point components; it would be useful to understand whether it follows from a more general physical principle or can be replaced by a weaker condition.

— Infrared Consistency and the Uniqueness of String Amplitudes  (2610.02124 - Huang et al., 1 Oct 2026) in Section 7, Summary and discussion