Quantum geometry of the universal hypermultiplet
arXiv:hep-th/0111080 · doi:10.1002/1521-3978(200209)50:8/9<909::AID-PROP909>3.0.CO;2-J
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.
6 pages, LaTeX; invited talk at the RTN meeting, Corfu, September 2001