The Omega Deformation, Branes, Integrability, and Liouville Theory

Abstract

We reformulate the Omega-deformation of four-dimensional gauge theory in a way that is valid away from fixed points of the associated group action. We use this reformulation together with the theory of coisotropic A-branes to explain recent results linking the Omega-deformation to integrable Hamiltonian systems in one direction and Liouville theory of two-dimensional conformal field theory in another direction.

96 pp

References in corpus (13)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• N=2 dualities
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• The quantum dilogarithm and representations quantum cluster varieties
• Surface Operators in N=2 4d Gauge Theories
• Loop operators and S-duality from curves on Riemann surfaces
• Higgs Bundles, Gauge Theories and Quantum Groups
• A-branes and Noncommutative Geometry
• Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I
• Gaudin model and opers
• Hitchin's connection, Toeplitz operators and symmetry invariant deformation quantization

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