Abstract
In [4] Balthazar, Rodriguez and Yin (BRY) computed the one instanton contribution to the two point scattering amplitude in two dimensional string theory to first subleading order in the string coupling. Their analysis left undetermined two constants due to divergences in the integration over world-sheet variables, but they were fixed by numerically comparing the result with that of the dual matrix model. If we consider n-point scattering amplitudes to the same order, there are actually four undetermined constants in the world-sheet approach. We show that using string field theory we can get finite unambiguous values of all of these constants, and we explicitly compute three of these four constants. Two of the three constants determined this way agree with the numerical result of BRY within the accuracy of numerical analysis, but the third constant seems to differ by 1/2. We also discuss a shortcut to determining the fourth constant if we assume the equality of the quantum corrected D-instanton action and the action of the matrix model instanton. This also agrees with the numerical result of BRY.
Highlights
Introduction and summaryD-instantons represent saddle points of the path integral in second quantized string theory and give non-perturbative contribution to the string amplitudes
We find the relations between the coordinates of the moduli space of Riemann surfaces and the parameters arising from string field theory description for various amplitudes
The usual world-sheet description of string amplitudes involves integration over moduli spaces of Riemann surfaces with punctures, with the external closed string vertex operators inserted at the punctures in the bulk of the world-sheet and the external open string vertex operators inserted at the punctures on the boundary of the world-sheet
Summary
D-instantons represent saddle points of the path integral in second quantized string theory and give non-perturbative contribution to the string amplitudes. This determines the function fdiv(ω1, ω2) leading to the result given in the second line of (1.18). This determines gdiv(ω), given in the first line of (1.18). The appendices describe the details of some of the computations whose results were used in the text
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