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First-Order Equations of Motion for Heterotic String Field Theory

We consider the equations of motion of the full heterotic string field theory including both the Neveu-Schwarz and the Ramond sectors. It is shown that they can be formulated in the form of an infinite number of first-order equations for an infinite number of independent string fields. We prove that the conventional equations of motion are obtaned by solving the extra equations for the extra string fields with a certain assumptions at the linearized level. The conventional gauge transformations are also obtained from those in this first-order formulation, which is clarified by deriving some lower oder transformations explicitly.