Variations on stability

TL;DR

The paper investigates stability of non-abelian D-branes beyond the large-volume limit by introducing Hitchin-like deformations to the standard stability conditions. It derives deformed vortex/Hermitian–Yang–Mills-type equations that couple gauge fields, transverse scalars, and tachyon data, and recasts them in a superconnection framework. A twisting of the theory to reformulate scalars as (0,1)-forms yields Hitchin-type equations and a modified stability concept, including a spectral-cover perspective via coverings and $X$-invariant subbranes. The work further connects brane–antibrane tachyons to the characteristic polynomial of transverse scalars, providing a unified geometric-physical picture and suggesting integrable-structure implications for the brane moduli space.

Abstract

We explore the effects of non-abelian dynamics of D-branes on their stability and introduce Hitchin-like modifications to previously-known stability conditions. The relation to brane-antibrane systems is used in order to rewrite the equations in terms of superconnections and arrive at deformed vortex equations.