$ \mathcal{N} = 2 $ instanton effective action in Ω-background and D3/D(−1)-brane system in R-R background

Abstract

We study the relation between the ADHM construction of instantons in the Ω-background and the fractional D3/D(−1)-branes at the orbifold singularity of $ \mathbb{C} \times {{{{\mathbb{C}^2}}} \left/ {{{\mathbb{Z}_2}}} \right.} $ in Ramond-Ramond (R-R) 3-form field strength background. We calculate disk amplitudes of open strings connecting the D3/D(−1)-branes in certain R-R background to obtain the D(−1)-brane effective action deformed by the R-R background. We show that the deformed D(−1)-brane effective action agrees with the instanton effective action in the Ω-background.