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

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} × {{{{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.