D-brane annihilation, renormalization-group flow and non-linear $\sigma$-model for the ADHM construction

TL;DR

This paper explores D-brane annihilation in type I string theory using a probe D1-brane, revealing how tachyon condensation leads to D5-branes and connecting the process to a non-linear sigma model related to the ADHM construction.

Contribution

It introduces a covariant formulation of D-brane annihilation, deriving conditions for tachyon fields that produce D5-branes and linking the process to a non-linear sigma model for the ADHM construction.

Findings

Tachyon condensation results in D5-branes as remnants.

The theory aligns with a non-linear sigma model related to ADHM.

Constraints on the background tachyon field are derived.

Abstract

In this note $D9$- and anti-$D9$-brane annihilation in type I string theory is probed by a $D1$-brane. We consider the covariant Green-Schwarz or twistor formulation of the probe theory. We expect the theory to be $\kappa$-invariant after the annihilation is completed. Conditions of the $\kappa$-invariance of the theory impose constraints on the background tachyon field. Solutions to the constraints define tachyon values which correspond to type I $D5$-branes as remnants of the annihilation. As a byproduct we get a theory which lies in the same universality class as the non-linear $\sigma$-model for the Atiyah-Drinfeld-Hitchin-Manin construction.