Normalization of Type IIB D-instanton Amplitudes

Abstract

We compute the normalization of single D-instanton amplitudes in type IIB string theory and show that the result agrees with the prediction of S-duality due to Green and Gutperle.

Muti-instanton Amplitudes in Type IIB String Theory

“…Direct computation of these amplitudes suffers from certain ambiguities related to integration over zero modes. Recently these ambiguities were resolved using string field theory [4] and the resulting leading term in the one instanton contribution to the amplitude was shown to agree with the predictions of [1,2]. Our goal in this paper will be to extend the results to multiinstanton amplitudes.…”

“…Our goal in this paper will be to extend the results to multiinstanton amplitudes. We shall not attempt to make the paper self-contained, but assume familiarity with the analysis of [4] and freely use the results of that paper.…”

“…We begin by computing the normalization constant that multiplies the k-instanton amplitude. As in [4], this is formally given by the exponential of the annulus diagram multiplied by i. Taking into account the effect of the k × k Chan-Paton factor, the annulus amplitude should be given by k 2 times the result for a single instanton.…”

“…with T 0 = I k / √ k representing the U(1) generator. Proceeding as in [4], we get the analog of eq. (4.32) of [4]:…”

“…We have dropped the multiplier factor ζ that appeared in [4] since there it was shown to be unity. The next step is to find the relation between the modes ξ 0 µ and the center of mass coordinate ξ µ of the D-instanton system.…”