String Field Theory as World-sheet UV Regulator

Even at tree level, the first quantized string theory suffers from apparent short distance singularities associated with collision of vertex operators that prevent us from straightforward numerical computation of various quantities. Examples include string theory S-matrix for generic external momenta and computation of the spectrum of string theory under a marginal deformation of the world-sheet theory. The former requires us to define the S-matrix via analytic continuation or as limits of contour integrals in complexified moduli space, while the latter requires us to use an ultraviolet cut-off at intermediate steps. In contrast, string field theory does not suffer from such divergences. In this paper we show how string field theory can be used to generate an explicit algorithm for computing tree level amplitudes in any string theory that does not suffer from any short distance divergence from integration over the world-sheet variables. We also use string field theory to compute second order mass shift of string states under a marginal deformation without having to use any cut-off at intermediate steps. We carry out the analysis in a broad class of string field theories, thereby making it manifest that the final results are independent of the extra data that go into the formulation of string field theory. We also comment on the generalization of this analysis to higher genus amplitudes.