Abstract
Type IIA string theory compactified on a Calabi-Yau threefold has a hypermultiplet moduli space whose metric is known to receive non-perturbative corrections from Euclidean D2-branes wrapped on 3-cycles. These corrections have been computed earlier by making use of mirror symmetry, S-duality and twistorial description of quaternionic geometries. In this paper we compute the leading corrections in each homology class using a direct world-sheet approach without relying on any duality symmetry or supersymmetry. Our results are in perfect agreement with the earlier predictions.
Highlights
D-instantons describe classical saddle points in type II and type I string theories and give non-perturbative contributions to string amplitudes
Type IIA string theory compactified on a Calabi-Yau threefold has a hypermultiplet moduli space whose metric is known to receive non-perturbative corrections from Euclidean D2-branes wrapped on 3-cycles
For this reason most of the initial study of D-instanton amplitudes, carried out in ten-dimensional type IIB string theory, used an indirect approach based on S-duality of this theory [2, 3]
Summary
D-instantons describe classical saddle points in type II and type I string theories and give non-perturbative contributions to string amplitudes. It is important to test this procedure by computing other amplitudes where the result is known, e.g., D-instanton corrections to the hypermultiplet moduli space in type II string theories on CY 3-folds. This is the problem that we shall address in this paper. This includes conventions for the world-sheet theory underlying ten-dimensional type IIA string theory as well as some details of compactification on CY 3-folds and its complex structure moduli space. Some of the technical details required for the analysis of this section, e.g. determination of certain phases and signs, the construction of the RR vertex operator in different pictures and some identities involving covariantly constant spinors in CY 3-folds are relegated to appendices
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