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

The N=2⁎ supersymmetric gauge theory is a massive deformation of N=4 , in which the adjoint hypermultiplet gets a mass. We present a D-brane realisation of the (non-)Abelian 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 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 Ω -background, in agreement with a recent proposal.