Deformation dynamics and the Gauss-Bonnet topological term in string theory

We show that there exist a nontrivial contribution on the Witten covariant phase space when the Gauss-Bonnet topological term is added to the Dirac-Nambu Goto action describing strings, because of the geometry of deformations is modified, and on such space we construct a symplectic structure. Future extensions of the present results are outlined.