Abstract
D-instanton amplitudes suffer from various infrared divergences associated with tachyonic or massless open string modes, leading to ambiguous contribution to string amplitudes. It has been shown previously that string field theory can resolve these ambiguities and lead to unambiguous expressions for D-instanton contributions to string amplitudes, except for an overall normalization constant that remains undetermined. In this paper we show that string field theory, together with the world-sheet description of the amplitudes, can also fix this normalization constant. We apply our analysis to the special case of two dimensional string theory, obtaining results in agreement with the matrix model results obtained by Balthazar, Rodriguez and Yin.
Highlights
JHEP11(2021)077 divergences in the amplitudes, the natural expectation would be that string field theory should be able to give an unambiguous result for the normalization constant
In this paper we show that string field theory, together with the world-sheet description of the amplitudes, can fix this normalization constant
We apply this procedure to the case of two dimensional string theory, and find that the normalization of the one instanton amplitude determined this way agrees with the results of the matrix model computed in [3] following the general formalism developed in [14]
Summary
Our goal is to compute the normalization constant N appearing in the D-instanton amplitudes. Since θ has period 2π, in order to determine the range of θ integral, we need to find the relation between θ and θ This in turn can be determined by comparing the string field theory gauge transformation law generated by θ to the rigid U(1) gauge transformation with parameter θ for any state of the open string that connects the D-instanton to the second D-instanton. We shall work in the convention in which the kinetic term of the open string fields has go independent normalization, so that in the Siegel gauge the quadratic part of the action is go independent, in agreement with the go independent exponent appearing in (2.7) In this convention, each open string vertex operator carries a factor of go.
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