Jan Louis, Roberto Valandro
We revisit the duality between heterotic string theory compactified on K3 x
T^2 and type IIA compactified on a Calabi-Yau threefold X in the hypermultiplet
sector. We derive an explicit map between the field variables of the respective
moduli spaces at the level of the classical effective actions. We determine the
parametrization of the K3 moduli space consistent with the Ferrara-Sabharwal
form. From the expression of the holomorphic prepotential we are led to
conjecture that both X and its mirror must be K3 fibrations in order for the
type IIA theory to have an heterotic dual. We then focus on the region of the
moduli space where the metric is expressed in terms of a prepotential on both
sides of the duality. Applying the duality we derive the heterotic
hypermultiplet metric for a gauge bundle which is reduced to 24 point-like
instantons. This result is confirmed by using the duality between the heterotic
theory on T^3 and M-theory on K3. We finally study the hyper-Kaehler metric on
the moduli space of an SU(2) bundle on K3.
View original:
http://arxiv.org/abs/1112.3566
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