### Abstract

The non-perturbative quantum geometry of the universal hypermultiplet (UH) is investigated in N = 2 supergravity. The UH low-energy effective action is given by the four-dimensional quaternionic non-linear sigma-model having an U(1) × U(1) isometry. The UH metric is governed by the single real pre-potential that is an eigenfunction of the Laplacian in the hyperbolic plane. We calculate the classical pre-potential corresponding to the standard (Ferrara-Sabharwal) metric of the UH arising in the Calabi-Yau compactification of type-II superstrings. The non-perturbative quaternionic metric, describing the D-instanton contributions to the UH geometry, is found by requiring the SL(2,Z) modular invariance of the UH pre-potential. The pre-potential found is unique, while it coincides with the D-instanton function of Green and Gutperle, given by the order-3/2 Eisenstein series. As a by-product, we prove cluster decomposition of D-instantons in curved spacetime. The non-perturbative UH pre-potential interpolates between the perturbative (large CY volume) region and the superconformal (Landau Ginzburg) region in the UH moduli space. We also calculate a non-perturbative scalar potential in the hyper-Kähler limit, when an abelian isometry of the UH metric is gauged in the presence of D-instantons.

Original language | English |
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Pages (from-to) | 365-388 |

Number of pages | 24 |

Journal | Nuclear Physics B |

Volume | 649 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 20 Jan 2003 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*649*(1-2), 365-388. https://doi.org/10.1016/S0550-3213(02)01026-X