Numerical Hermitian Yang-Mills connections and Kähler cone substructure

Anderson, Lara B., Braun, Volker and Ovrut, Burt A. (2011) Numerical Hermitian Yang-Mills connections and Kähler cone substructure. Journal of High Energy Physics, 2012 (1). ISSN 1029-8479

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We further develop the numerical algorithm for computing the gauge connection of slope-stable holomorphic vector bundles on Calabi-Yau manifolds. In particular, recent work on the generalized Donaldson algorithm is extended to bundles with Kähler cone substructure on manifolds with h^1,1 > 1. Since the computation depends only on a one-dimensional ray in the Kähler moduli space, it can probe slope-stability regardless of the size of h^1,1 . Suitably normalized error measures are introduced to quantitatively compare results for different directions in Kähler moduli space. A significantly improved numerical integration procedure based on adaptive refinements is described and implemented. Finally, an efficient numerical check is proposed for determining whether or not a vector bundle is slope-stable without computing its full connection.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 05 Oct 2017 19:26
Last Modified: 14 Dec 2022 15:17
Identification Number: DIAS-STP-11-14

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