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 Ünsal 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 numerical result recently found in the literature.

Figure 1

Comparison of the barrier factor $F(N)=-\log (\mathrm{\Gamma }/V)$ (in units of $10^6$) given by Eq. (1) at $\theta =0$ (solid) with the fit to the numerical data of Ref. [5], $F(N)=a(N+c{)}^b$ with $a=3.906\times 10^{-3}$, $b=4.83304$, $c=4.26324$ (dashed).