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

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 if 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-algebra, should find applications to algebraic geometry where there is no canonical choice of stable geometrical objects. (C) 2004 Elsevier B.V. All rights reserved.