Abstract
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.
Highlights
N = 2 supersymmetric theories, with two four-dimensional (4d) supercharges, provide a simple and interesting playground for studying exact dynamics of gauge theories, their couplings to supergravity and various dualities
N = 2 topological strings describe the coupling of topological field theories to gravity and its partition function computes a series of higher dimensional F-terms, FgW 2g, involving powers of the chiral Weyl superfield W in the effective N = 2 supergravity action [3,4]
In this work we present a string realisation of an Abelian 5d and 4d N = 2∗ theory1 and compute the couplings Fg,n of a double series of higher-dimensional F-terms of the form W 2g n, where is the chiral projection of a certain anti-chiral vector superfield with lower component corresponding to the self-dual field strength. This amounts to compute a series of amplitudes involving four gravitini, 2g − 2 anti-self-dual graviphotons and n self-dual gauge fields belonging to the multiplet of the D5-brane coupling modulus
Summary
In this work we present a string realisation of an Abelian 5d and 4d N = 2∗ theory and compute the couplings Fg,n of a double series of higher-dimensional F-terms of the form W 2g n, where is the chiral projection of a certain anti-chiral vector superfield with lower component corresponding to the self-dual field strength. This amounts to compute a series of amplitudes involving four gravitini, 2g − 2 anti-self-dual graviphotons and n self-dual gauge fields belonging to the multiplet of the D5-brane coupling modulus. We consider the simple Scherk– Schwarz deformation since it allows for an exact CFT description which is amenable to concrete perturbative computations
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