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

In this note the D9-and anti-D9-brane annihilation in the type I string theory is probed by the D1-brane. We consider covariant Green-Schwarz formulation of the probe theory. For it to be non-anomalous it is necessary to consider the number of the D9-branes to be by 32 bigger than that of anti-D9-branes. Also for the anomaly cancellation it is necessary to insist on the κ-invariance of the D1-brane action. As the result the tachyon field should obey some constraints. Solutions to the latter define tachyon values which correspond to the type I D5-branes as remnants of the annihilation. By product we get a theory which lies in the same universality class as the non-linear σ-model for the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction.