Brane-Antibrane Systems on Calabi-Yau Spaces

TL;DR

This paper establishes a mathematical correspondence between brane-antibrane systems and stable triples, linking physical configurations to stability conditions in algebraic geometry, and explores implications for BPS states and higher-dimensional branes.

Contribution

It introduces a novel correspondence between brane-antibrane systems and stable triples, connecting physical models to mathematical stability conditions and proposing new insights into BPS states.

Findings

Reduction of field equations to vortex equations under holomorphicity

Equivalence of vortex equations to stability of triples

Identification of new BPS bound states and relations to higher-dimensional branes

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.