Space-time locality in the $Sp(2)$-symmetric Lagrangian formalism

The existence of a local solution to the $Sp(2)$ master equation for the gauge field theory is proved in the perturbation theory under standard regularity assumptions for the action. The arbitrariness of solutions to the $Sp(2)$ master equation is described, provided they are proper. The effective action can be chosen to be $Sp(2)$ invariant and (under the additional assumption that the gauge transformation generators are Lorentz tensors) Lorentz invariant.