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

Abstract

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 $θ$, 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.

Figures (1)

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