Determine the physical origin of antipodal self-duality

Determine the physical origin of antipodal self-duality in planar supersymmetric Yang–Mills theory and related fishnet theories.

Background

Antipodal self-duality (ASD) relates an amplitude or form factor to itself after a kinematic transformation and application of the antipode of the Hopf algebra of multiple polylogarithms. The paper emphasizes that ASD has been observed in very few processes, including the four-point form factor of the chiral stress-tensor operator in planar supersymmetric Yang–Mills theory and square fishnet integrals.

Although the paper develops new examples and provides an integrability-based construction of ASD combinations of ladder integrals, it does not explain why ASD occurs physically. Identifying its origin is presented as a motivation for studying neighboring integrable theories.

References

Given that there is really only one example of ASD in pMSYM, and that its physical origin is unknown, it is worth searching for more examples in neighboring theories.

— Antipodal Self-Duality for Generalized Fishnets from Integrability  (2610.00803 - Dixon et al., 30 Sep 2026) in Section 1, Introduction