The Omega Deformation From String and M-Theory

Abstract

We present a string theory construction of Omega-deformed four-dimensional gauge theories with generic values of ε_1 and ε_2. Our solution gives an explicit description of the geometry in the core of Nekrasov and Witten's realization of the instanton partition function, far from the asymptotic region of their background. This construction lifts naturally to M-theory and corresponds to an M5-brane wrapped on a Riemann surface with a selfdual flux. Via a 9-11 flip, we finally reinterpret the Omega deformation in terms of non-commutative geometry. Our solution generates all modified couplings of the Ω-deformed gauge theory, and also yields a geometric origin for the quantum spectral curve of the associated quantum integrable system.

LaTeX, 35 pages, 1 figure. Appendix on couplings of hypermultiplets in N=4 SYM added

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• Worldsheet Realization of the Refined Topological String
• Classical Yang-Baxter Equation from Supergravity
• Generalized type IIB supergravity equations and non-Abelian classical r-matrices
• M-theory in the Omega-background and 5-dimensional non-commutative gauge theory
• A slow review of the AGT correspondence
• Deformed Seiberg-Witten Curves for ADE Quivers
• Modular anomaly equations in N=2* theories and their large-N limit
• Tri-vector deformations in $d=11$ supergravity
• BPS States in Omega Background and Integrability
• M-Theoretic Derivations of 4d-2d Dualities: From a Geometric Langlands Duality for Surfaces, to the AGT Correspondence, to Integrable Systems
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• A 5d/3d duality from relativistic integrable system
• Deformed supersymmetric gauge theories from the fluxtrap background
• Compactification on the Ω-background and the AGT correspondence
• Superspin chains from superstring theory
• Monopole Quivers and new 3D N=2 dualities
• Integrable Superstrings on the Squashed Three-sphere
• Bands and gaps in Nekrasov partition function
• Alpha- and Omega-Deformations from fluxes in M-Theory
• Yang-Baxter deformations and generalized supergravity -- A short summary
• Yang-Baxter deformations of Minkowski spacetime
• Omega-Deformed Seiberg-Witten Effective Action from the M5-brane
• On the large $\Omega$-deformations in the Nekrasov-Shatashvili limit of $\mathcal{N}=2^{\ast }$ SYM
• Probing the Moduli Dependence of Refined Topological Amplitudes
• Twisted holography of defect fusions
• BPS States in the Duality Web of the Omega deformation
• Torsion and Supersymmetry in Omega-background
• Non-integrability of the $\Omega$-deformation
• Killing spinors from classical r-matrices
• Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2$ theories
• Twisted N=4 Super Yang-Mills Theory in Omega-background
• Embedding Integrable Superspin Chain in String Theory
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours
• Gravity Dual of Two-Dimensional $\mathcal{N}=(2,2{)}^{\ast }$ Supersymmetric Yang-Mills Theory and Integrable Models
• Topological AdS/CFT and the $\Omega$ deformation
• A string realisation of $\Omega$-deformed Abelian $\mathcal{N}=2^{\ast }$ theory
• Extended Gauge Theory Deformations From~Flux~Backgrounds
• Solution of quantum integrable systems from quiver gauge theories
• SUSY and tri-vector deformations
• Exponential Networks for Linear Partitions
• The String Geometry Behind Topological Amplitudes
• Refined Topological Amplitudes from the $\Omega$-Background in String Theory
• Line Operators in 4d Chern-Simons Theory and Cherkis Bows
• The braneology of 3D dualities
• A stringy perspective on the quantum integrable model/gauge correspondence
• BPS Equations in Omega-deformed N=4 Super Yang-Mills Theory