New Aspects of Heterotic--F Theory Duality

TL;DR

This paper explores the duality between Heterotic string theory and F-theory, providing new insights into matter multiplets, Yukawa couplings, and the geometric translation of physical features via refined duality mappings.

Contribution

It introduces a detailed translation of matter multiplets and fluxes between Heterotic and F-theory, refining the duality dictionary and linking spectral surfaces to F-theory singularities.

Findings

Chiral matter multiplets are sections of line bundles on covering matter curves.

Chirality is expressed through fluxes in F-theory.

Divisors correspond to codimension-3 singularities in F-theory.

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^x 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 M2-branes wrapped on a vanishing two-cycle propagate in F-theory. Chirality formulae are given purely in terms of (possibly 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.