Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves

Abstract

We study the dynamics of a N=2 supersymmetric SU(N) gauge theory with fundamental or adjoint matter in presence of a non trivial Omega-background along a two dimensional plane. The prepotential and chiral correlators of the gauge theory can be obtained, via a saddle point analysis, from an equation which can be viewed as a non commutative version of the "standard" Seiberg and Witten curve.

arXiv comment35 pages, 3 figures, minor corrections. version to appear in JHEP with the correction of a tex error

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• S-duality as a beta-deformed Fourier transform
• A Solvable Deformation of Quantum Mechanics
• Exact WKB Analysis of N = 2 Gauge Theories
• Deformed Seiberg-Witten Curves for ADE Quivers
• Modular anomaly equations in N=2* theories and their large-N limit
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• Quantum Hitchin Systems via beta-deformed Matrix Models
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• Refined geometric transition and $qq$-characters
• Quantum Spin Systems and Supersymmetric Gauge Theories, I
• Holomorphic field realization of SH${}^c$ and quantum geometry of quiver gauge theories
• Quantum geometry from the toroidal block
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
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• Modular and duality properties of surface operators in N=2* gauge theories
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• Wilson Loops and Chiral Correlators on Squashed Spheres
• Finite ${\epsilon }_2$-corrections to the $\mathcal{N}=2$ SYM prepotential
• Non-perturbative studies of N=2 conformal quiver gauge theories
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• VEV of Baxter's Q-operator in N=2 gauge theory and the BPZ differential equation
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• Notes on Mayer Expansions and Matrix Models
• Mayer expansion of the Nekrasov pre potential: the subleading ${\epsilon }_2$-order
• Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2$ theories
• Classical Liouville Three-point Functions from Riemann-Hilbert Analysis
• More on the SW-QNM correspondence
• Quantum integrability of $\mathcal{N}=2$ 4d gauge theories
• Effective Gravitational Couplings of Higher-Rank Supersymmetric Gauge Theories
• Seiberg-Witten period relations in Omega background
• Deformed planar topological open string amplitudes on Seiberg-Witten curve
• On a path integral representation of the Nekrasov instanton partition function and its Nekrasov--Shatashvili limit
• VEV of $Q$-operator in $U(1)$ linear quiver 5d gauge theories
• Effective Gravitational Couplings of Kaluza-Klein Gauge Theories
• Deformed SW curve and the null vector decoupling equation in Toda field theory
• On non-stationary Lamé equation from WZW model and spin-1/2 XYZ chain