The Omega Deformation, Branes, Integrability, and Liouville Theory
Nikita Nekrasov, Edward Witten
TL;DR
This paper presents a new formulation of the Omega-deformation in gauge theory, connecting it to integrable systems and Liouville theory through coisotropic A-branes, expanding understanding of its mathematical structure.
Contribution
It introduces a reformulation of the Omega-deformation valid away from fixed points and links it to integrability and Liouville theory via coisotropic A-branes.
Findings
Reformulation of Omega-deformation away from fixed points
Connection established between Omega-deformation, integrable systems, and Liouville theory
Use of coisotropic A-branes to explain these links
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.
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