Virtues of a symmetric-structure double copy
John Joseph M. Carrasco, Nicolas H. Pavao
Abstract
We demonstrate a physical motivation for extending color-dual or Bern-Carrasco-Johansson (BCJ) double-copy construction to include theories with kinematic numerators that obey the same algebraic relations as symmetric structure constants, ${d}^{abc}=\mathrm{Tr}[{{T}^{a},{T}^{b}}{T}^{c}]$. We verify that $U({N}_{c})$ 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 nonadjoint kinematics.