  We explore, at the nonperturbative level, the large $N$ equivalence between
ordinary $SU(N)$ Yang-Mills theory on $\mathbb{R}^4$ and on $\mathbb{R}^3
\times S^1$ with double-trace deformations. In particular, we compare the
values of the $0^{++}$ glueball mass obtained in both sides of the equivalence.
