Renormalizing handles and holes in string theory

We discuss loop corrections to string equations of motion in the framework of Wilsons renormalization group (RG). In a cutoff field theory defined on the world sheet a RG transformation also means integrating out small handles or holes. This modifies the RG flow equations and hence its fixed points. A finite cutoff enables us to treat all string modes in a unified fashion. A novel feature of our approach is a direct demonstration of mixing of various string modes at the loop level.