Heterotic–type IIA duality with fluxes

Abstract

In this paper we study a possible non-perturbative dual of the heterotic string compactified on K3 × T 2 in the presence of background fluxes. We show that type IIA string theory compactified on manifolds with SU (3) structure can account for a subset of the possible heterotic fluxes. This extends our previous analysis to a case of a non-perturbative duality with fluxes.

Flux-induced isometry gauging in heterotic strings

“…We wil provide an exact matching between the flux parameters [9,13,11]. Then we show a theorem due to Witten guarantees the protection of gauged isometries.…”

“…We will begin by recalling the results in [11,13]. The anomaly cancellation in the 10d supergravity requires we modify the heterotic H in the following way,…”

“…Comparing (3.8) with (2.3), we immediately see that the gauging from the gauge fluxes does not correspond to any H or F in IIA theory. But the effect can be dualized into the gauging coming from the torsions in the geometry; it is dual to IIA on an SU (3) × SU (3) structure manifold [11]. For a review on SU (3) × SU (3) structure manifolds in the context of supergravity, see [6].…”

“…The study of mirror symmetry for Calabi-Yau flux compactification, for instance, will inevitably lead us to the territory of "Non-Kählerity" [2,3,4,5,6,7] It is also very interesting to study the fate of the well-known IIA/hetrotic string duality if we compactify IIA string on the non-Kähler background. This nonpertubative duality between IIA on K3 fibered Calabi-Yau and heterotic string on K3×T 2 was first studied in [8,9] and then generalized to the case with fluxes and SU (3)-structure manifolds [13,11].…”

“…A worldsheet instanton wrapping a holomorphic cycle in K3, for example, could give correction to the hyper moduli space because there are hypermultiplets coming from H 2 (K3). However, the isometry gauging is achieved by turning on the abelian gauge fluxes over certain 2 cycle C in K3 [11], which means the gauge bundle restricted to the 2 cycle V | C is non-trivial. This is precisely the situation where the instanton correction is zero [20].…”