### Abstract

Some instanton corrections to the universal hypermultiplet moduli space metric of the type IIA string theory compactified on a Calabi-Yau threefold arise due to multiple wrapping of BPS membranes and five-branes around certain cycles of Calabi-Yau. The classical universal hypermultipet metric is locally equivalent to the Bergmann metric of the symmetric quaternionic space SU(2,1)/U(2), whereas its generic quaternionic deformations are governed by the integrable SU(∞) Toda equation. We calculate the exact (non-perturbative) UH metrics in the special cases of (i) the D-instantons (the wrapped D2-branes) in the absence of five-branes, and (ii) the five-brane instantons with vanishing charges, in the absence of D-instantons. The solutions of the first type preserve the U(1)×U(1) classical symmetry, while they can be interpreted as the gravitational dressing of the hyper-Kähler D-instanton solutions. The solutions of the second type preserve the non-abelian SU(2) classical symmetry, while they can be interpreted as the gradient flows in the universal hypermultiplet moduli space.

Original language | English |
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Pages (from-to) | 256-280 |

Number of pages | 25 |

Journal | Nuclear Physics B |

Volume | 604 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 18 Jun 2001 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*604*(1-2), 256-280. https://doi.org/10.1016/S0550-3213(01)00184-5