# A string realisation of $\varOmega$-deformed Abelian $\mathcal{N}=2^*$ theory

## TL;DR

This paper presents a D-brane construction of the $
abla$-deformed Abelian $
math{N}=2^*$ theory, deriving topological amplitudes that match the Nekrasov partition function in the $
abla$-background, linking string theory and gauge theory results.

## Contribution

It introduces a string-theoretic D-brane realization of the $
abla$-deformed $
math{N}=2^*$ theory and computes topological amplitudes matching gauge theory predictions.

## Key findings

- Reproduces Nekrasov partition function in the $
abla$-background.
- Provides a string theory derivation of $
abla$-deformed gauge theories.
- Expresses amplitudes as a double series expansion with physical couplings.

## Abstract

The $\mathscr{N}=2^*$ supersymmetric gauge theory is a massive deformation of $\mathscr{N}=4$, in which the adjoint hypermultiplet gets a mass. We present a D-brane realisation of the (non-)Abelian $\mathscr{N}=2^*$ theory, and compute suitable topological amplitudes, which are expressed as a double series expansion. The coefficients determine couplings of higher-dimensional operators in the effective supergravity action that involve powers of the anti-self-dual $\mathscr{N}=2$ chiral Weyl superfield and of self-dual gauge field strengths superpartners of the D5-brane coupling modulus. In the field theory limit, the result reproduces the Nekrasov partition function in the two-parameter $\varOmega$-background, in agreement with a recent proposal.