On the closed bosonic string effective action

We have analyzed the closed bosonic string effective action to all orders in string loops. Using the proper-time regularization of the local logarithmic infinities, we propose a renormalization scheme valid for all genera, which leaves only a dilaton potential as higher string-loop corrections to the partition function. We assume the string is propagating in a genus-dependent background in such a way that the physical (renormalized) background fields are genus-independent. After subtraction of modular infinities, the string-loop corrections to the β-functions are only cosmological terms. (orig.)