Moduli in N=1 heterotic/F-theory duality

TL;DR

This paper explores the duality between heterotic and F-theory compactifications in four dimensions, analyzing moduli spaces through geometric objects and cohomology, revealing deep correspondences and new insights into their structure.

Contribution

It provides a detailed geometric interpretation of heterotic and F-theory moduli, establishing isomorphisms between their associated abelian varieties and extending the understanding of duality.

Findings

Identification of heterotic moduli with cohomology groups of spectral covers

Establishment of an isomorphism between heterotic Prym and F-theoretic intermediate Jacobian

Generalization of heterotic 5brane / F-theoretic 3brane impurity matching

Abstract

The moduli in a 4D N=1 heterotic compactification on an elliptic CY, as well as in the dual F-theoretic compactification, break into "base" parameters which are even (under the natural involution of the elliptic curves), and "fiber" or twisting parameters; the latter include a continuous part which is odd, as well as a discrete part. We interpret all the heterotic moduli in terms of cohomology groups of the spectral covers, and identify them with the corresponding F-theoretic moduli in a certain stable degeneration. The argument is based on the comparison of three geometric objects: the spectral and cameral covers and the ADE del Pezzo fibrations. For the continuous part of the twisting moduli, this amounts to an isomorphism between certain abelian varieties: the connected component of the heterotic Prym variety (a modified Jacobian) and the F-theoretic intermediate Jacobian. The comparison of the discrete part generalizes the matching of heterotic 5brane / F-theoretic 3brane impurities.