String Field Theory as World-sheet UV Regulator

Understand

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.