Extending the geometry of heterotic spectral cover constructions

Lara B. Anderson (Department of Physics, Virginia Tech, Blacksburg, USA) ; Xin Gao (College of Physics, Sichuan University, Chengdu, China) ; Mohsen Karkheiran (Department of Physics, Virginia Tech, Blacksburg, USA)

In this work we extend the well-known spectral cover construction first developed by Friedman, Morgan, and Witten to describe more general vector bundles on elliptically fibered Calabi-Yau geometries. In particular, we consider the case in which the Calabi-Yau fibration is not in Weierstrass form, but can rather contain fibral divisors or multiple sections (i.e. a higher rank Mordell-Weil group). In these cases, general vector bundles defined over such Calabi-Yau manifolds cannot be described by ordinary spectral data. To accomplish this we employ well established tools from the mathematics literature of Fourier-Mukai functors. We also generalize existing tools for explicitly computing Fourier-Mukai transforms of stable bundles on elliptic Calabi-Yau manifolds. As an example of these new tools we produce novel examples of chirality changing small instanton transitions. The goal of this work is to provide a geometric formalism that can substantially increase the understood regimes of heterotic/F-theory duality.

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Published on:
14 July 2020
Publisher:
Elsevier
Published in:
Nuclear Physics B , Volume 956 C (2020)

Article ID: 115003
DOI:
https://doi.org/10.1016/j.nuclphysb.2020.115003
Copyrights:
The Authors
Licence:
CC-BY-3.0

Fulltext files: