We obtain the effective action for the bosonic string with arbitrary
Yang-Mills fields, up to the \alpha' order, in general dimensions. The form of
the action is determined by the requirement that the action admit well-defined
Killing spinor equations, whose projected integrability conditions give rise to
the full set of equations of motion. The success of the construction suggests
that the hidden "pseudo-supersymmetry" associated with the Killing spinor
equations may be a property of the bosonic string itself.Comment: 9 page
