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

Abstract

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.

v3: Minor revision; 14 pages

References in corpus (9)

• Fivebranes, Membranes and Non-Perturbative String Theory
• Nonlinear Instantons from Supersymmetric p-Branes
• The spectrum of BPS branes on a noncompact Calabi-Yau
• On the algebras of BPS states
• D-branes, open string vertex operators, and Ext groups
• D-Branes and Bundles on Elliptic Fibrations
• Kahler Cone Substructure
• Stability Conditions For Topological D-branes: A Worldsheet Approach
• Variations on stability

Cited by in corpus (6)

• Loop-Corrected Compactifications of the Heterotic String with Line Bundles
• Supersymmetric (non-)Abelian Bundles in the Type I and SO(32) Heterotic String
• Non-Abelian Brane Worlds: The Heterotic String Story
• Topological D-Branes and Commutative Algebra
• Heterotic Vacua from general (non-) Abelian Bundles
• Elliptic mirror of the quantum Hall effect