Metastable vacuum decay in center-stabilized Yang-Mills theory at large N

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.