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Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic

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Michael R. Douglas1,2, Robert L. Karp1, Sergio Lukic1 and René Reinbacher1

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We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian Einstein metrics on the tangent bundle and a rank three vector bundle on Bbb P2. In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic.

Keywords

Differential and Algebraic Geometry

Statistical Methods

 

E-print Number: hep-th/0606261

Cited: by |

Refers: to

PACS

11.15.-q Gauge field theories

11.25.Mj Compactification and four-dimensional models

Subjects

Particle physics and field theory

Dates

Issue 12 (December 2007)

Received 28 November 2007, accepted for publication 14 December 2007

Published 20 December 2007



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