Theta dependence of the deconfining phase transition in pure SU(N_c) Yang-Mills theories

Abstract

Recently, it has been conjectured that deconfining phase transition in SU(N_c) pure Yang-Mills theories is continuously connected to a quantum phase transition in softly broken N=1 super Yang-Mills on R^{1,2}*S^1. We exploit this conjecture to study the strength of the transition and deconfining temperature as a function of the vacuum angle theta in pure Yang-Mills. We find that the transition temperature is a decreasing function of theta in [0, π), in an excellent agreement with recent lattice simulations. We also predict that the transition becomes stronger for the same range of theta, and comment on the theta dependence in the large N_c limit. More lattice studies are required to test our predictions.

Figures (3)

• Figure 1: The $N_c=3$ and $\theta=\pi/2$ effective potential $V_{\hbox{\scriptsize np}}$ (in units of $V_{\hbox{\scriptsize bion}}^0$) as a function of $\chi_3$ for $\chi_2=\chi_4=0$, and $\chi_1\cong 0$.
• Figure 2: The critical normalized deconfinement temperature $\frac{T^{\hbox{\scriptsize cr}}(\theta)}{T^{\hbox{\scriptsize cr}}(0)}$. The vacuum branch is $k=0$ for $\theta \in (-\pi,\pi)$, and $k=2$ for $\theta \in (\pi, 3\pi)$. We find that $\frac{T^{\hbox{\scriptsize cr}}(\theta)}{T^{\hbox{\scriptsize cr}}(0)}$ is a periodic function of $\theta$ with period $2\pi$, and cusps at $\theta=(2n+1)\pi$ for any integer $n$, where two branches become degenerate.
• Figure 3: The normalized discontinuity of the holonomy $\Gamma(\theta)/\Gamma(0)=\Delta\left|\frac{g^2}{4\pi N_c}\hbox{tr}\Omega(\theta)\right|/\Delta\left|\frac{g^2}{4\pi N_c}\hbox{tr}\Omega(0)\right|$. We take $\theta$ in the range $(-\pi, 3\pi)$, and $N_c=3$. The vacuum branch is $k=0$ for $\theta \in (-\pi,\pi)$, and $k=2$ for $\theta \in (\pi, 3\pi)$. We find that $\Gamma(\theta)/\Gamma(0)$ is a periodic function of $\theta$ with period $2\pi$, and cusps at $\theta=(2n+1)\pi$ for any integer $n$, where two branches become degenerate.