Abstract

We compute the contribution of Euclidean D-branes in type IIB string theory on Calabi-Yau threefolds to the metric on the hypermultiplet moduli space in the large volume, weak coupling limit. Our results are in perfect agreement with the predictions based on S-duality, mirror symmetry and supersymmetry.

Highlights

  • Type II string theories are known to receive non-perturbative contributions from Euclidean D-branes wrapped on compact cycles

  • In a previous paper [1], extending the results of [2,3,4], we computed these corrections to the hypermultiplet moduli space metric in type IIA string theory compactified on Calabi-Yau (CY) threefolds in the weak coupling limit and compared the results with the predictions based on S-duality, mirror symmetry and supersymmetry [5,6,7]

  • As we will see, the actual computation in type IIB string theory has a somewhat different flavor and different subtleties than those encountered in the analysis of type IIA string theory

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Summary

Introduction

Type II string theories are known to receive non-perturbative contributions from Euclidean D-branes wrapped on compact cycles These contributions are expected to play an important role in stabilizing the moduli in semi-realistic string compactifications and the determination of Yukawa couplings in the low energy effective field theory. This case is somewhat different from the systems analyzed in type IIA string theory in [1], where the Euclidean branes were assumed to be rigid, with the only moduli being associated with the motion along the non-compact directions and the fermion zero modes associated with broken supersymmetry. The appendices contain various technical results that are used in the analysis in the main text

Conventions
Classical hypermultiplet moduli space
Normalization of the fields
Prediction for the D-instanton amplitude
D-instantons in type IIB
The leading instanton contribution
Strategy for computing instanton correction to the metric
Explicit computation of Dp-brane corrections
NSNS axion contribution
Dilaton contribution
RR contributions
D1-brane
D3-brane
D5-brane
Final result
Non-linear terms
Disk amplitude with one RR field and a pair of zero modes
Disk amplitude with one NSNS field and a pair of zero modes
Multiple-charge system
A Manifestly S-duality invariant metric
B Kähler moduli space and holomorphic cycles
C Boundary condition on spin fields
D Normalization of the RR fields
E Vertex operator for the RR fields and string field theory action
F Normalization of the hypermultiplet moduli
G D-instanton action in the presence of NSNS 2-form field

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