# Exact partition functions for the Ω-deformed N=2∗$$\mathcal{N}={2}^{\ast }$$ SU(2) gauge theory

@article{Beccaria2016ExactPF,
title={Exact partition functions for the $\Omega$-deformed N=2∗\$\$ \mathcal\{N\}=\{2\}^\{\ast \} \$\$ SU(2) gauge theory},
author={Matteo Beccaria and G. Macorini},
journal={Journal of High Energy Physics},
year={2016},
volume={2016},
pages={1-24}
}
• Published 1 June 2016
• Mathematics
• Journal of High Energy Physics
A bstractWe study the low energy effective action of the Ω-deformed N=2∗$$\mathcal{N}={2}^{\ast }$$ SU(2) gauge theory. It depends on the deformation parameters ϵ1, ϵ2, the scalar field expectation value a, and the hypermultiplet mass m. We explore the plane mϵ1ϵ2ϵ1$$\left(\frac{m}{\upepsilon_1},\frac{\upepsilon_2}{\upepsilon_1}\right)$$ looking for special features in the multi-instanton contributions to the prepotential, motivated by what happens in the Nekrasov-Shatashvili limit ϵ2 → 0…
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## References

SHOWING 1-10 OF 103 REFERENCES
On the large Ω-deformations in the Nekrasov-Shatashvili limit of N=2*$$\mathcal{N}={2}^{*}$$ SYM
A bstractWe study the multi-instanton partition functions of the Ω-deformed N=2*$$\mathcal{N}={2}^{*}$$ SU(2) gauge theory in the Nekrasov-Shatashvili (NS) limit. They depend on the deformation
S-duality and the prepotential in N=2⋆$$\mathcal{N}={2}^{\star }$$ theories (I): the ADE algebras
• Mathematics
• 2015
A bstractThe prepotential of N=2⋆$$\mathcal{N}={2}^{\star }$$ supersymmetric theories with unitary gauge groups in an Ω background satisfies a modular anomaly equation that can be recursively
S-duality, triangle groups and modular anomalies in N=2$$\mathcal{N}=2$$ SQCD
• Mathematics
• 2016
A bstractWe study N=2$$\mathcal{N}=2$$ superconformal theories with gauge group SU(N ) and 2N fundamental flavours in a locus of the Coulomb branch with a ℤN$${\mathbb{Z}}_N$$ symmetry. In this
Stringy instanton corrections to $\mathcal{N} = 2$ gauge couplings
• Mathematics, Physics
• 2010
We discuss a string model where a conformal four-dimensional $\mathcal{N} = 2$ gauge theory receives corrections to its gauge kinetic functions from “stringy” instantons. These contributions are
S-duality and the prepotential of N=2⋆$$\mathcal{N}={2}^{\star }$$ theories (II): the non-simply laced algebras
• Mathematics
• 2015
A bstractWe derive a modular anomaly equation satisfied by the prepotential of the N=2⋆$$\mathcal{N}={2}^{\star }$$ supersymmetric theories with non-simply laced gauge algebras, including the
Modular anomaly equations in N$$\mathcal{N}$$ =2* theories and their large-N limit
• Physics
• 2014
A bstractWe propose a modular anomaly equation for the prepotential of the N$$\mathcal{N}$$ =2* super Yang-Mills theory on ℝ4 with gauge group U(N) in the presence of an Ω-background. We then study
Deformed $\mathcal{N}=2$ theories, generalized recursion relations and S-duality
• Mathematics
• 2013
A bstractWe study the non-perturbative properties of $\mathcal{N}=2$ super conformal field theories in four dimensions using localization techniques. In particular we consider SU(2) gauge theories,
Lectures on instanton counting
• Mathematics
• 2003
These notes have two parts. The first is a study of Nekrasov's deformed partition functions $Z(\ve_1,\ve_2,\vec{a}:\q,\vec{\tau})$ of N=2 SUSY Yang-Mills theories, which are generating functions of
Classical torus conformal block, $\mathcal{N}$ = 2∗ twisted superpotential and the accessory parameter of Lamé equation
A bstractIn this work the correspondence between the semiclassical limit of the DOZZ quantum Liouville theory on the torus and the Nekrasov-Shatashvili limit of the $\mathcal{N}$ = 2∗ (Ω-deformed)
Exact results in $\mathcal{N}=2$ gauge theories
• Mathematics
• 2013
A bstractWe derive exact formulae for the partition function and the expectation values of Wilson/’t Hooft loops, thus directly checking their S-duality transformations. We focus on a special class