What is meant by the symbol $\mathbb{R}^2_{\hbar}$?

Question

I am reading some papers in mathematical physics (https://arxiv.org/pdf/1006.0977.pdf) and I came across the following symbol $\mathbb{R}^2_{\hbar}$ I don't recognize nor could I find any background information on. It has something to do with regularizing the euclidean plane $\mathbb{R}^2$ using equivariant cohomology so that you may compactify on it. Does anyone know the name of such a space? Would it be called an equivariant euclidean plane for instance? Any insight in how this equivariance process works is greatly appreciated as well!

Thanks in advance.

Answer 1

It's the $\Omega$-background. The definition is in the same paper you are reading, in the appendix A at page 61.