Exact nonlinear constraints for gauge–gravity coupled systems

Determine the exact identity that generates the nonlinear constraints on single-trace and double-trace Wilson coefficients in gauge–gravity coupled systems, with the aim of characterizing the constraints whose numerical bounds may isolate heterotic and infinite-spin-tower theories.

Background

The paper derives all-order nonlinear master equations for four-point amplitudes in maximally supersymmetric Yang–Mills theory and supergravity from six-point consistency, scalar parity, and discrete R-symmetry. It notes that analogous nonlinear constraints have recently been found for gauge–gravity coupled systems, where single-trace and double-trace Wilson coefficients mix in the gluon sector.

The authors leave unresolved the exact identity underlying those constraints. Establishing it could extend the infrared consistency framework beyond the separate gauge-theory and supergravity settings studied in the paper and clarify numerical indications associated with heterotic and infinite-spin-tower theories.

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.

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