Virtues of a symmetric-structure double copy

Abstract

We demonstrate a physical motivation for extending color-dual or BCJ double-copy construction to include theories with kinematic numerators that obey the same algebraic relations as symmetric structure constants, d^{abc}=Tr[{T^a,T^b}T^c]. We verify that U(N) nonlinear sigma model (NLSM) pions, long known to be color-dual in terms of antisymmetric adjoint factors, f^{abc}, are also color-dual in the sense of symmetric color structures, d^{abc}, explicitly through six-point scattering. This reframing of NLSM pion amplitudes complements our compositional construction of d^{abc} color-dual higher derivative gauge operators. With adjoint and symmetric color-dual kinematics, we can span all four-point effective photon operators via a double-copy construction using amplitudes from physical theories. We further comment on a tension between locality and adjoint effective numerators, and the implications for spanning gravitational effective operators with non-adjoint kinematics.