F-theory and linear sigma models

TL;DR

This paper develops a method to translate between linear sigma models and spectral cover descriptions of stable bundles on elliptic Calabi-Yau manifolds, advancing understanding of heterotic/F-theory duality.

Contribution

It introduces an explicit translation method between linear sigma models and spectral cover descriptions, and explores heterotic/F-theory duality in four dimensions.

Findings

Spectral bundle contains essential heterotic information.

Dual gauge theory on F-theory 7-branes encodes heterotic data.

Method for analyzing vector bundle stability and splitting over elliptic curves.

Abstract

We present an explicit method for translating between the linear sigma model and the spectral cover description of SU(r) stable bundles over an elliptically fibered Calabi-Yau manifold. We use this to investigate the 4-dimensional duality between (0,2) heterotic and F-theory compactifications. We indirectly find that much interesting heterotic information must be contained in the `spectral bundle' and in its dual description as a gauge theory on multiple F-theory 7-branes. A by-product of these efforts is a method for analyzing semistability and the splitting type of vector bundles over an elliptic curve given as the sheaf cohomology of a monad.