IPMU11-0096 String theory of the Omega deformation

Abstract

This paper is dedicated to the memory of the victims of the Tohoku earthquake and tsunami of March 2011. 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 super-symmetric NS fluxbrane background. We furthermore note that this background is the string theoretic realization of an Ω deformation of flat space in the directions transverse to the branes where the deformation parameters satisfy ε1 = −ε2. This Ω deforma-tion 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 re-produce 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. a