Instanton calculus in R-R background and the topological string

TL;DR

This paper uses string theory techniques to analyze gauge instantons in N=2 super Yang-Mills theory within a R-R background, connecting instanton calculus with topological string theory and the Omega-background.

Contribution

It provides a string theory derivation of the instanton prepotential and elucidates its relation to topological strings and the Omega-background.

Findings

Computed the instanton prepotential using string theory methods.

Established the equivalence with topological string results.

Clarified the connection to the Omega-background.

Abstract

We study a system of fractional D3 and D(-1) branes in a Ramond-Ramond closed string background and show that it describes the gauge instantons of N=2 super Yang-Mills theory and their interactions with the graviphoton of N=2 supergravity. In particular, we analyze the instanton moduli space using string theory methods and compute the prepotential of the effective gauge theory exploiting the localization methods of the instanton calculus showing that this leads to the same information given by the topological string. We also comment on the relation between our approach and the so-called Omega-background.