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Abstract
We use the twistorial construction of D-instantons in Calabi-Yau compactifications of type II string theory to compute an explicit expression for the metric on the hypermultiplet moduli space affected by these non-perturbative corrections. In this way we obtain an exact quaternion-Kähler metric which is a non-trivial deformation of the local c-map. In the four-dimensional case corresponding to the universal hypermultiplet, our metric fits the Tod ansatz and provides an exact solution of the continuous Toda equation. We also analyze the fate of the curvature singularity of the perturbative metric by deriving an S-duality invariant equation which determines the singularity hypersurface after inclusion of the D(-1)-instanton effects.
Highlights
To stabilize all moduli and to get a viable cosmological models [1], they provide resolution of unphysical singularities in the moduli space [2], and they appear to be a crucial ingredient ensuring various stringy dualities [3, 4]
If one includes only electrically charged D-instantons (in the type IIA formulation these are instantons coming from D2-branes wrapping A-cycles in H3(Y, Z), whereas in type IIB they correspond to D(-1) and D1-instantons), the obtained metric is valid to all orders in the instanton expansion and it is an exact quaternion-Kahler metric
It is known as the c-map metric which gives a canonical construction of a QK manifold as a bundle over a special Kahler base
Summary
At tree level the metric on MH is obtained by Kaluza-Klein reduction from tendimensional supergravity and turns out to be determined by the prepotential F [29, 30] It is known as the c-map metric which gives a canonical construction of a QK manifold as a bundle over a special Kahler base. −2 Im FΛΣ, the matrix is its inverse, c χY 192π is the deformation parameter encoding the one-loop correction, and AK is the so-called Kahler connection on sKc. Topologically the metric (2.2) describes a bundle with the two-stage fibration structure. Jc(Y) is the so-called intermediate Jacobian with the special Kahler base parametrized by complex structure moduli za and with the fiber given by the torus of RR-fields, Tζ,ζ = H3(Y, R)/H3(Y, Z).
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