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Quantum geometry of the universal hypermultiplet

✍ Scribed by Sergei V. Ketov

Publisher: John Wiley and Sons
Year: 2002
Tongue: English
Weight: 101 KB
Volume: 50
Category: Article
ISSN: 0015-8208
DOI: 10.1002/1521-3978(200209)50:8/9<909::aid-prop909>3.0.co;2-j

No coin nor oath required. For personal study only.

✦ Synopsis

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 Painlevé VI equation.

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