Brane-Antibrane Systems on Calabi-Yau Spaces

TL;DR

The paper establishes a geometric bridge between brane-antibrane systems on Calabi–Yau spaces and stable holomorphic triples $ (E_1,E_2,T) $, identifying the tachyon as a map between bundles and showing that holomorphicity reduces the dynamics to vortex equations. A precise correspondence is drawn: solutions to the vortex equations are in one-to-one correspondence with $\sigma$-stable triples, providing a stability-based framework to classify BPS bound states and their tachyon condensation to lower-dimensional branes. Concrete examples (e.g., D0-branes on $\mathbb{C}$ and branes wrapped on holomorphic cycles) illustrate how exact sequences and cokernels encode localized brane charges, while connections to stable sheaves and quiver stability illuminate the relationships to Hitchin-type equations and K-theory. The work further shows how dimensional reduction on $X\times\mathbb{P}^1$ links triple stability to stability of $SU(2)$-invariant bundles, clarifying when supersymmetric bound states exist and how they relate to wrapped higher-dimensional branes. Overall, the framework provides a robust, mathematically precise lens to study brane-antibrane physics, tachyon condensation, and BPS spectra through stability conditions and complex-analytic data.

Abstract

We propose a correspondence between brane-antibrane systems and stable triples (E_1,E_2,T), where E_1,E_2 are holomorphic vector bundles and the tachyon T is a map between them. We demonstrate that, under the assumption of holomorphicity, the brane-antibrane field equations reduce to a set of vortex equations, which are equivalent to the mathematical notion of stability of the triple. We discuss some examples and show that the theory of stable triples suggests a new notion of BPS bound states and stability, and curious relations between brane-antibrane configurations and wrapped branes in higher dimensions.