Induced Rigid String Action from Fermions

By adding the Dirac action on the world sheet, an effective action is obtained by integrating over the four-dimensional fermion fields pulled back to the world sheet. This action consists of the Nambu–Goto area term with a right dimensionful constant in front, extrinsic curvature action, and the topological Euler characteristic term. The divergent coefficients in front of these terms are absorbed in the rigid string action without fermions.