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arXiv · hep-th/0111080

Quantum geometry of the universal hypermultiplet

Sergei V. Ketov
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Abstract

The universal hypermultiplet moduli space metric in the type-IIA superstring theory compactified on a Calabi-Yau threefold is related to integrable systems. The instanton corrections in four dimensions arise due to multiple wrapping of BPS membranes and fivebranes around certain (supersymmetric) cycles of Calabi-Yau. The exact (non-perturbative) metrics can be calculated in the special cases of (i) the D-instantons (or the wrapped D2-branes) in the absence of fivebranes, and (ii) the fivebrane instantons with vanishing charges, in the absence of D-instantons. The solutions of the first type are governed by the three-dimensional Toda equation, whereas the solutions of the second type are governed by the particular Painleve VI equation.

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Sergei V. Ketov. 2001-11-08. Quantum geometry of the universal hypermultiplet. https://doi.org/10.1002/1521-3978(200209)50%3A8%2F9%3C909%3A%3Aaid-prop909%3E3.0.co%3B2-j

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