N = 2 heterotic-type II duality and bundle moduli

Heterotic string compactifications on a K 3 surface S $$ \mathfrak{S} $$ depend on a choice of hyperkähler metric, anti-self-dual gauge connection and Kalb-Ramond flux, parametrized by hypermultiplet scalars. The metric on hypermultiplet moduli space is in principle computable within the (0, 2) superconformal field theory on the heterotic string worldsheet, although little is known about it in practice. Using duality with type II strings compactified on a Calabi-Yau threefold, we predict the form of the quaternion-Kähler metric on hypermultiplet moduli space when S $$ \mathfrak{S} $$ is elliptically fibered, in the limit of a large fiber and even larger base. The result is in general agreement with expectations from Kaluza-Klein reduction, in particular the metric has a two-stage fibration structure, where the B -field moduli are fibered over bundle and metric moduli, while bundle moduli are themselves fibered over metric moduli. A more precise match must await a detailed analysis of R 2 -corrected ten-dimensional supergravity