Instanton Calculus in R-R 3-form Background and Deformed N=2 Super Yang-Mills Theory

TL;DR

This paper explores the effects of a constant R-R 3-form background on instantons in N=2 super Yang-Mills theory, comparing string theory and gauge theory approaches, and analyzing the resulting deformations and equations of motion.

Contribution

It introduces a deformed instanton effective action in R-R backgrounds and compares it with D-brane effective actions, revealing discrepancies and proposing improvements.

Findings

Discrepancy at second order in deformation parameters.

Improved deformed action with space-time dependent gauge coupling.

Same instanton equations of motion at lowest order despite differences.

Abstract

We study the ADHM construction of instantons in N=2 supersymmetric Yang-Mills theory deformed in constant Ramond-Ramond (R-R) 3-form field strength background in type IIB superstrings. We compare the deformed instanton effective action with the effective action of fractional D3/D(-1) branes at the orbifold singularity of C^2/Z_2 in the same R-R background. We find discrepancy between them at the second order in deformation parameters, which comes from the coupling of the translational zero modes of the D(-1)-branes to the R-R background. We improve the deformed action by adding a term with space-time dependent gauge coupling. Although the space-time action differs from the action in the omega-background, both actions lead to the same instanton equations of motion at the lowest order in gauge coupling.