N=2 Heterotic-Type II duality and bundle moduli

Sergey Alexandrov (1) , Jan Louis (2) , Boris Pioline (3, 4) , Roberto Valandro (5)

1 L2C - Laboratoire Charles Coulomb
2 Fachbereich Physik [Hamburg]
3 CERN [Genève]
4 LPTHE - Laboratoire de Physique Théorique et Hautes Energies
5 ICTP - Abdus Salam International Centre for Theoretical Physics [Trieste]

Heterotic string compactifications on a $K3$ surface $\mathfrak{S}$ 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 $\mathfrak{S}$ 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.

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Sergey Alexandrov, Jan Louis, Boris Pioline, Roberto Valandro. N=2 Heterotic-Type II duality and bundle moduli. Journal of High Energy Physics, 2014, 08, pp.092. ⟨10.1007/JHEP08(2014)092⟩. ⟨hal-01006533⟩