New aspects of Heterotic–F-theory duality

Abstract

In order to understand both up-type and down-type Yukawa couplings, F-theory is a better framework than the perturbative Type IIB string theory. The duality between the Heterotic and F-theory is a powerful tool in gaining more insights into F-theory description of low-energy chiral multiplets. Because chiral multiplets from bundles ∧ 2 V and ∧ 2 V × as well as those from a bundle V are all involved in Yukawa couplings in Heterotic compactification, we need to translate descriptions of all those kinds of matter multiplets into F-theory language through the duality. We find that chiral matter multiplets in F-theory are global holomorphic sections of line bundles on what we call covering matter curves. The covering matter curves are formulated in Heterotic theory in association with normalization of spectral surface, while they are where M 2-branes wrapped on a vanishing two-cycle propagate in F-theory. Chirality formulae are given purely in terms of primitive four-form flux. In order to complete the translation, the dictionary of the Heterotic-F theory duality has to be refined in some aspects. A precise map of spectral surface and complex structure moduli is obtained, and with the map, we find that divisors specifying the line bundles correspond precisely to codimension-3 singularities in F-theory.

The Tate form on steroids: resolution and higher codimension fibers

“…Again, we observe that additional surface components appear in the fiber, which therefore ceases to be flat. This is easily seen as the resolved geometry (4.4) along b 2 = 0 has the form 14) which shows that the following loci are completely contained inside the fiber…”

F-theory on all toric hypersurface fibrations and its Higgs branches

“…String backgrounds constructed via F-theory are not only located in the heart of the web of string dualities, but also allow for the construction of phenomenologically appealing local GUT-models [4][5][6][7], which has recently rekindled a lot of interest into the subject. The basic idea of F-theory is to replace the axio-dilaton τ = C 0 + ie −φ , that is only defined up to SL(2, Z)-transformations, by a quantity, that only depends on the SL(2, Z)-equivalence class of τ .…”

“…5 For the search of an F-theory realization of these theories it is crucial to construct new classes of Calabi-Yau manifolds X admitting new geometric features and to deduce the general SUGRA theories that arise in F-theory compactifications on these X. 6 There has been a lot of recent progress in systematically extending the set of CalabiYau manifolds X that can be used for F-theory compactifications. The different approaches can be roughly sorted into two groups.…”

Phenomenological implications of a minimal F-theory GUT with discrete symmetry

“…Hence, old successful GUTs based on the exceptional groups E 6,7,8 , as well as the lower rank SO (10) and SU(5) ones, can be naturally realised as effective F-theory models. As such, they constitute a particularly promising component of the vast string landscape, since many parameters of the effective low energy models are determined from a few basic A pictorial representation of a Calabi fourfold, which exhibits elliptic fibration over a threefold base, B 3 .…”