Numerical Hermitian Yang-Mills connections and vector bundle stability in heterotic theories

Anderson, Lara B. and Braun, Volker and Karp, Robert L. and Ovrut, Burt A. (2010) Numerical Hermitian Yang-Mills connections and vector bundle stability in heterotic theories. Journal of High Energy Physics, 2010 (6). ISSN 1029-8479

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Official URL: http://doi.org/10.1007/JHEP06(2010)107

Abstract

A numerical algorithm is presented for explicitly computing the gauge connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds. To illustrate this algorithm, we calculate the connections on stable monad bundles defined on the K3 twofold and Quintic threefold. An error measure is introduced to determine how closely our algorithmic connection approximates a solution to the Hermitian Yang-Mills equations. We then extend our results by investigating the behavior of non slope-stable bundles. In a variety of examples, it is shown that the failure of these bundles to satisfy the Hermitian Yang-Mills equations, including field-strength singularities, can be accurately reproduced numerically. These results make it possible to numerically determine whether or not a vector bundle is slope-stable, thus providing an important new tool in the exploration of heterotic vacua.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 05 Oct 2017 19:25
Last Modified: 26 Jul 2018 10:01
URI: http://dair.dias.ie/id/eprint/257

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