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Non-linear Yang-Mills instantons from strings are $π$-stable D-branes

H. Enger·C. A. Lütken
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Abstract

We show that B-type $Π$-stable D-branes do not in general reduce to the (Gieseker-) stable holomorphic vector bundles used in mathematics to construct moduli spaces. We show that solutions of the almost Hermitian Yang--Mills equations for the non-linear deformations of Yang--Mills instantons that appear in the low-energy geometric limit of strings exist iff they are $π$-stable, a geometric large volume version of $Π$-stability. This shows that $π$-stability is the correct physical stability concept. We speculate that this string-canonical choice of stable objects, which is encoded in and derived from the central charge of the string-\emph{algebra}, should find applications to algebraic geometry where there is no canonical choice of stable \emph{geometrical} objects.

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H. Enger, C. A. Lütken. 2004-06-01. Non-linear Yang-Mills instantons from strings are $π$-stable D-branes. https://doi.org/10.1016/j.nuclphysb.2004.06.051

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