String theory of the Omega deformation

TL;DR

This paper constructs a supersymmetric real mass deformation for D2-brane gauge theories using string theory backgrounds, revealing an Omega-deformation that impacts the dynamics and solutions of the system.

Contribution

It introduces a string-theoretic realization of the Omega-deformation as a background for D2-branes, connecting it to gauge theory and spin-chain correspondences.

Findings

Derived BPS solutions in the deformed background

Established the string theory realization of Omega-deformation

Linked the deformation to gauge theory and spin-chain models

Abstract

In this article, we construct a supersymmetric real mass deformation for the adjoint chiral multiplets in the gauge theory describing the dynamics of a stack of D2-branes in type II string theory. We do so by placing the D2-branes into the T-dual of a supersymmetric NS fluxbrane background. We furthermore note that this background is the string theoretic realization of an Omega-deformation of flat space in the directions transverse to the branes where the deformation parameters satisfy \epsilon_1 = - \epsilon_2. This \Omega-deformation therefore serves to give supersymmetric real masses to the chiral multiplets of the 3D gauge theory. To illustrate the physical effect of the real mass term, we derive BPS-saturated classical solutions for the branes rotating in this background. Finally, we reproduce all the same structure in the presence of NS fivebranes and comment on the relationship to the gauge theory/spin-chain correspondence of Nekrasov and Shatashvili.