K3-fibrations and heterotic-type II string duality

Abstract

We analyze the map between heterotic and type II N=2 supersymmetric string theories for certain two and three moduli examples found by Kachru and Vafa. The appearance of elliptic j-functions can be traced back to specializations of the Picard-Fuchs equations to systems for K 3 surfaces. For the three-moduli example we write the mirror maps and Yukawa couplings in the weak coupling limit in terms of j-functions; the expressions agree with those obtained in perturbative calculations in the heterotic string in an impressive way. We also discuss symmetries of the world-sheet instanton numbers in the type II theory, and interpret them in terms of S-duality of the non-perturbative heterotic string.

Instanton numbers and exchange symmetries in N = 2 dual string pairs

“…Subsequent work connected this symmetry to the monodromy group of the CY compactification [13,14] and discussed [15] the action of this exchange symmetry on BPS spectra and higher derivative gravitational couplings. In this paper, we will extend the previous work of [6,12,13,16,17,18] in several directions. We will focus on a class of type II theories based on elliptically fibered CY spaces.…”

“…In the following we will be concerned with N = 2, D = 4 string theories which have both a heterotic and a type II description [6,12]. In this context, there is a particularly interesting class of models, which exhibits a non-perturbative symmetry which exchanges the heterotic dilaton S with one of the vector moduli fields.…”

“…In this context, there is a particularly interesting class of models, which exhibits a non-perturbative symmetry which exchanges the heterotic dilaton S with one of the vector moduli fields. In the context of heterotic/type II string/string duality this type of exchange symmetry was first discussed in [12], where this exchange symmetry was related to a a remarkle symmetry property of rational instanton numbers. Subsequent work connected this symmetry to the monodromy group of the CY compactification [13,14] and discussed [15] the action of this exchange symmetry on BPS spectra and higher derivative gravitational couplings.…”

Self-dual strings and N = 2 supersymmetric field theory

“…This is obvious for type IIA compactifications on K3-fibered threefolds in [18] that are of Fermat form, whose type IIB mirrors can be written as…”

Flux-induced isometry gauging in heterotic strings

“…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].…”