N=4 instanton calculus in Ω and R-R backgrounds

We study the instanton calculus for N=4 super Yang-Mills theory in ten-dimensional Ω-background with the R-symmetry Wilson line gauge field. From the ADHM construction of instantons in the background, we obtain the deformed instanton effective action. For a certain case we get the effective action of N=2⁎ theory in the Ω-background. We also study the low-energy effective D(−1)-brane action for the D3/D(−1)-brane system in the R-R 3-form field strength backgrounds and find that the action agrees with the instanton effective action in the Ω-background.