Deformed BPS Monopole in Omega-background

TL;DR

This paper investigates deformed BPS monopoles in Omega-background, deriving new equations, solutions, and properties, including an explicit monopole profile, within deformed supersymmetric gauge theories.

Contribution

It introduces the deformed BPS monopole equation in Omega-background, finds axially-symmetric solutions, and explicitly constructs a monopole profile, revealing the monopole charge remains undeformed.

Findings

Deformed BPS equation has axially-symmetric solutions.

Monopole charge remains undeformed in the Omega-background.

Explicit one-monopole solution and profile are constructed.

Abstract

We study the BPS condition in the $\Omega$-deformed $\mathcal{N}=2$ super Yang-Mills theory when one of the $\epsilon$-parameters of the background is zero. We obtain the deformed BPS equation for dyons and the formula for their central charge. In particular, we find that the deformed BPS monopole equation has axially-symmetric solution and is equivalent to the Ernst equation. The monopole charge is shown to be undeformed. We construct one-monopole solution explicitly and examine its profile.