Abstract
Abstract Heterotic string theory compactified on a K3 surface times T 2 is believed to beequivalent to type II string theory on a suitable Calabi-Yau threefold. In particular, it must share the same hypermultiplet moduli space. Building on the known twistorial description on the type II side, and on recent progress on the map between type II and heterotic moduli in the limit where both the type II and heterotic strings become classical, we provide a new twistorial construction of the hypermultiplet moduli space in this limit which is adapted to the symmetries of the heterotic string. We also take steps towards understanding the twistorial description for heterotic worldsheet instanton corrections away from the classical limit. As a spin-off, we obtain a twistorial description of a class of automorphic forms of SO(4, n, $\mathbb{Z}$ ) obtained by Borcherds’ lift.
Highlights
Infinite volume on the type IIB side, and compared with the expected result on the heterotic side
Building on the known twistorial description on the type II side, and on recent progress on the map between type II and heterotic moduli in the limit where both the type II and heterotic strings become classical, we provide a new twistorial construction of the hypermultiplet moduli space in this limit which is adapted to the symmetries of the heterotic string
We develop a twistorial description of the HM moduli space MH which is adapted to the symmetries of the heterotic string on S, in particular to the automorphism group SO(3, n − 1, Z) of the lattice of two-cycles on S and to large gauge transformations of the B-field
Summary
At zeroth order in the string coupling constant, the HM moduli space MH in type IIB string theory compactified on a threefold Yis obtained from the Kahler moduli space MK of Yby the c-map construction [47, 48]. H1,1(Y )) measure the periods of the complexified Kahler form B + iJ on a basis γa of the homology lattice H2(Y , Z), dual to a basis γa of H4(Y , Z) under the cup product. In the limit where the base is very large, the prepotential takes the form. In the limit where the area Im zs of the base is very large, the prepotential (2.1) reduces to the leading, cubic term, while the Kahler potential (2.3) takes the form. Note that (M −1)AB = M AB where the indices are raised and lowered by the matrix ηAB This identifies the metric (2.2) in the limit Re (s) → +∞ as the c-map of the special Kahler space. Will become apparent shortly, that the c-map of this space is the orthogonal Wolf space W(n) [50]
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