Universality of the entanglement-selection rule under alternative deformations

Determine whether deformations of the gluon and graviton four-point vertices other than the specific minimal tree-level deformation adopted in the analysis obey the same genuine-tripartite-entanglement selection rule favoring the gauge-invariant or diffeomorphism-invariant theory.

Background

The paper studies a particular symmetry-breaking prescription in which only the four-point interaction is deformed while the free kinetic term and transverse helicity degrees of freedom remain unchanged. Within this prescription, the gauge-invariant theory for gluon scattering and the diffeomorphism-invariant theory for graviton scattering are favored by suppression of genuine tripartite entanglement in the forward and backward limits.

The authors explicitly note that gauge invariance can be broken in many inequivalent ways. It remains unresolved whether the observed entanglement-based selection rule is universal across alternative deformations of the four-point vertex or depends on the specific deformation used in the paper.