Yang-Mills kinematic algebra via homotopy transfer from a worldline operator algebra

The homotopy Lie or $L_{\mathrm{\infty }}$ algebra encoding Yang-Mills theory is the tensor product of a color Lie algebra with the kinematic $C_{\mathrm{\infty }}$ algebra. We derive this $C_{\mathrm{\infty }}$ algebra, via homotopy transfer, from a strict operator algebra of a worldline theory, realized as an associative star product algebra. This gives a homotopy transfer interpretation to worldline vertex operators introduced in previous work.