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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 × 2/2 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.

= 2 Instanton Effective action in Ω-background and D3/D(−1)-brane System in R-R background