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

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 κ-invariant after the annihilation is completed. Conditions of the κ-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 σ-model for the Atiyah–Drinfeld–Hitchin–Manin construction.