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

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

2003-12-21

arxiv.org/abs/hep-th/0312254v3

Nucl.Phys. B695 (2004) 73-83

Physics

High Energy Physics

High Energy Physics - Theory

v3: Minor revision; 14 pages

Scientific paper

10.1016/j.nuclphysb.2004.06.051

We show that B-type $\Pi$-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 $\pi$-stable, a geometric large volume version of $\Pi$-stability. This shows that $\pi$-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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