BPS Equations in Omega-deformed N=4 Super Yang-Mills Theory
Katsushi Ito, Yusuke Kanayama, Hiroaki Nakajima, Shin Sasaki

TL;DR
This paper investigates the effects of Omega-deformation on N=4 super Yang-Mills theory, deriving deformed BPS equations and analyzing supersymmetry and BPS states in a specific limit.
Contribution
It introduces deformed BPS equations in Omega-deformed N=4 SYM and explores supersymmetry and BPS states in the Nekrasov-Shatashvili limit.
Findings
Derived Omega-deformed 1/2 and 1/4 BPS dyon equations.
Computed the deformed central charge of the superalgebra.
Analyzed the structure of BPS states under Omega-deformation.
Abstract
We study supersymmetry of N=4 super Yang-Mills theory in four dimensions deformed in the Omega-background. We take the Nekrasov-Shatashvili limit of the background so that two-dimensional super Poincare symmetry is recovered. We compute the deformed central charge of the superalgebra and study the 1/2 and 1/4 BPS states. We obtain the Omega-deformed 1/2 and 1/4 BPS dyon equations from the deformed supersymmetry transformation and the Bogomol'nyi completion of the energy.
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