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

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 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-algebra, should find applications to algebraic geometry where there is no canonical choice of stable geometrical objects. [email protected] [email protected]