Summary: We consider lattice deformations (both continuous and topological) of the hexagonal lattice model describing the electronic wave function of graphene in the tight binding approximation. The deformation involves operators with the range up to next-to-neighbor. In the low energy limit, we find that these deformations give rise to couplings of the electronic Dirac field to an external scalar (Yukawa) and gauge fields. The fields are expressed in terms of original defects. As a by-product we establish that the next-to-nearest order is the minimal range of deformations which produces the complete gauge and scalar fields. We consider an example of Stone-Wales defect, and find the associated gauge field.