Effective interactions of the open bosonic string via field theory

We describe a method to extract an effective Lagrangian description for open bosonic strings, at zero transcendentality. The method relies on a particular formulation of its scattering amplitudes derived from color-kinematics duality. More precisely, starting from a (DF)² + YM quantum field theory, we integrate out all the massive degrees of freedom to generate an expansion in the inverse string tension α′. We explicitly compute the Lagrangian terms through $\mathcal{O}$ \( \mathcal{O} \) (α′⁴), and target the sector of operators proportional to F⁴ to all orders in α′.