Killing Spinors for the Bosonic String
  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. 
H. Lu and Zhao-Long Wang
hep-th