eventually for computing instanton corrections to the relevant correlation functions that determine the hypermultiplet quantum-geometry. The exact moduli space must be consistent with the results derived in our paper. In particular, our supergravity instanton solutions should match with the results obtained from wrapping branes in the full ten-dimensional string theory. Stated differently, the universal hypermultiplet metric must contain exponential corrections which, at leading order in the string coupling constant and $\alpha'$, agree with the form of our instanton action. Using some results about quaternionic geometry [@CP; @DWRV], it should be possible to find quaternionic metrics which asymptotically reproduce our results. We intend to report further on these issues in the near future.

Acknowledgements {#acknowledgements .unnumbered}
================

We thank Michael Gutperle and Thomas Mohaupt for discussions and reading an earlier draft of this paper. U.T. thanks the Deutsche Forschungsgemeinschaft for financial support.

SL(3,R) / SL(2,R) $\times$ SO(1,1) {#SL3R}
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In this appendix, we discuss some geometrical aspects related to the sigma model corresponding to , with target space . The easiest way to study this space is by using the fact that the Minkowskian version of the universal hypermultiplet moduli space is both Kähler and quaternion-Kähler. Since Kähler geometry is simpler 