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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 aD-brane realisation of the (non-)Abelian $\mathscr{N}=2^*$ theory, and computesuitable topological amplitudes, which are expressed as a double seriesexpansion. The coefficients determine couplings of higher-dimensional operatorsin the effective supergravity action that involve powers of the anti-self-dual$\mathscr{N}=2$ chiral Weyl superfield and of self-dual gauge field strengthssuperpartners of the D5-brane coupling modulus. In the field theory limit, theresult reproduces the Nekrasov partition function in the two-parameter$\varOmega$-background, in agreement with a recent proposal.

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