Closed string exchanges on $C^2/Z_2$ in a background B-field

TL;DR

This paper demonstrates how nonplanar two-point functions in a noncommutative gauge theory on a fractional D3 brane can be exactly reproduced by summing contributions from massless closed string exchanges in a $C^2/Z_2$ orbifold background with a B-field.

Contribution

It explicitly identifies the contributions of individual closed string modes to the IR singularities in the noncommutative gauge theory.

Findings

Massless closed string exchanges reproduce IR singularities.

Contributions from each closed string mode sum to the nonplanar two-point function.

Clarifies the role of closed string modes in noncommutative gauge theories.

Abstract

In an earlier work it was shown that the IR singularities arising in the nonplanar one loop two point function of a noncommutative ${\cal N}=2$ gauge theory can be reproduced exactly from the massless closed string exchanges. The noncommutative gauge theory is realised on a fractional $D_3$ brane localised at the fixed point of the $C^2/Z_2$ orbifold. In this paper we identify the contributions from each of the closed string modes. The sum of these adds upto the nonplanar two-point function.