The Omega Deformation From String and M-Theory

TL;DR

This paper constructs a string theory model of Omega-deformed 4D gauge theories, providing explicit geometric descriptions, a lift to M-theory, and connections to non-commutative geometry and quantum integrable systems.

Contribution

It offers a novel string and M-theory construction of Omega-deformed gauge theories with explicit geometric and flux configurations, linking to quantum spectral curves.

Findings

Explicit geometric description of Omega deformation in string theory

Lift to M-theory with M5-brane configuration

Connection to non-commutative geometry and quantum integrable systems

Abstract

We present a string theory construction of Omega-deformed four-dimensional gauge theories with generic values of \epsilon_1 and \epsilon_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 \Omega-deformed gauge theory, and also yields a geometric origin for the quantum spectral curve of the associated quantum integrable system.