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

Abstract

The $\mathcal{N}=2^{\ast }$ supersymmetric gauge theory is a massive deformation of $\mathcal{N}=4$, in which the adjoint hypermultiplet gets a mass. We present a D-brane realisation of the (non-)Abelian $\mathcal{N}=2^{\ast }$ 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 $\mathcal{N}=2$ 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 $\Omega$-background, in agreement with a recent proposal.

1+22 pages. v2 Author name corrected on the arXiv metadata