N=4 Instanton Calculus in Omega and R-R Backgrounds

TL;DR

This paper investigates the instanton calculus in N=4 super Yang-Mills theory within ten-dimensional Omega-backgrounds and R-R fields, deriving deformed effective actions and establishing connections with D-brane systems.

Contribution

It introduces a method to compute deformed instanton effective actions in Omega-backgrounds and R-R backgrounds, extending previous instanton calculus to new settings.

Findings

Derived the deformed instanton effective action in Omega-backgrounds.

Connected instanton calculus with D-brane effective actions in R-R backgrounds.

Showed agreement between D(-1)-brane and instanton effective actions.

Abstract

We study the instanton calculus for N=4 super Yang-Mills theory in ten-dimensional Omega-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 Omega-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 Omega-background.