Loop Corrected D-branes Stability Conditions

TL;DR

This paper investigates how string loop corrections modify D-brane stability conditions in type-II Calabi-Yau compactifications, leading to loop-corrected Hermitian-Yang-Mills and special Lagrangian conditions.

Contribution

It introduces loop corrections to D-brane stability conditions derived from topological string theory, extending classical stability criteria to include quantum effects.

Findings

Loop corrections modify the central charges of D-branes.

Loop-corrected Hermitian-Yang-Mills equation for B-type branes.

Loop-corrected special Lagrangian condition for A-type branes.

Abstract

In type-II string theory compactifications on Calabi-Yau manifolds, topological string theory partition functions give a class of exact F-terms in the four-dimensional effective action. We point out that in the background of constant self-dual field strength, these terms deform the central charges for D-branes wrapping Calabi-Yau manifold to include string loop corrections. We study the corresponding loop corrected D-brane stability conditions, which for B-type branes at the large volume limit implies loop corrected Hermitian-Yang-Mills equation, and for A-type branes imply loop corrected special Lagrangian submanifold condition.