Abstract
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.
Highlights
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
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
Theories with tachyons e.g. bosonic string theory and superstring theory formulated around certain non-supersymmetric backgrounds, give sensible results, our analysis will be valid for the corresponding string field theories
Summary
We shall briefly review some aspects of the world-sheet theory and the string field theory that we shall need for our analysis. We denote by ψμ and χ their holomorphic superpartners on the world-sheet — in type II theories we have anti-holomorphic fields ψμ and χ Their operator product expansions have the form:. In the bosonic string theory the physical unintegrated vertex operators take the form ccV where V is a dimension (1,1) primary in the matter CFT. In the heterotic string theory the unintegrated −1 picture NS sector vertex operator takes the form cce−φV ,. The precise choice of these subspaces, or the coordinate system in which the vertex operators are inserted, or the PCO locations are not fixed completely but are subject to stringent constraints, and different choices lead to different string field theories which are related by field redefinition Note that in this definition we do not require the Ai’s to be BRST invariant. We must replace Ψ by Ψ + ΨR in the second term in (2.19)
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