  We calculate the rate of the decay of a metastable vacuum state in $SU(N)$
gauge theory on ${\mathbb R}^3 \times {\mathbb S}^1$ space with a double trace
deformation suggested by \"Unsal and Yaffe. The derived analytical expression
for the exponential factor in the decay rate, including the dependence on the
parameter $\theta$, gives the exact behavior in the leading power of $N$ in the
limit of large $N$ and provides a better approximation than a recently found in
the literature numerical result.
