Numerical Hermitian Yang-Mills connections and vector bundle stability in heterotic theories
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 K 3 twofold and Quintic threefold. An error measure i...
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| Veröffentlicht in: | The journal of high energy physics 2010-06, Vol.2010 (6), Article 107 |
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| creator | Anderson, Lara B. Braun, Volker Karp, Robert L. Ovrut, Burt A. |
| description | 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
K
3 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. |
| doi_str_mv | 10.1007/JHEP06(2010)107 |
| format | Article |
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K
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K
3 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. 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K
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| subjects | Algorithms Bundles Bundling Classical and Quantum Gravitation Elementary Particles Error analysis High energy physics Mathematical analysis Numerical analysis Physics Physics and Astronomy Quantum Field Theories Quantum Field Theory Quantum Physics Relativity Theory String Theory |
| title | Numerical Hermitian Yang-Mills connections and vector bundle stability in heterotic theories |
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