Aspects of Open-Closed Duality in a Background B-Field II

It was shown in [hep-th/0503009], in the context of bosonic theory that the IR singular terms that arise as a result of integrating out high momentum modes in nonplanar diagrams of noncommutative gauge theory can be recovered from low lying tree-level closed string exchanges. This follows as a natural consequence of world-sheet open-closed string duality. Here using the same setup we study the phenomenon for noncommutative ${\cal N}=2$ gauge theory realised on a $D_3$ fractional brane localised at the fixed point of $C^2/Z_2$. The IR singularities from the massless closed string exchanges are exactly equal to those coming from one-loop gauge theory. This is as a result of cancellation of all contributions from the massive modes.