Induced Rigid String Action From Fermions
  From the Dirac action on the world sheet, an effective action is obtained by integrating over the 4-dimensional fermion fields pulled back to the world sheet. This action consists of the Nambu-Goto area term with right dimensionful constant in front, extrinsic curvature action and the topological Euler characteristic term. 
R.Parthasarathy and K.S.Viswanathan