A study of the 't Hooft loop in SU(2) Yang-Mills theory

TL;DR

In the deconfined phase T > T( c), the spatial 't Hooft loop exhibits a dual string tension, which vanishes at T(c) with a 3D Ising-like critical exponent.

Abstract

We study the behaviour of the spatial and temporal 't Hooft loop at zero and finite temperature in the 4D SU(2) Yang-Mills theory, using a new numerical method. In the deconfined phase $T>T_c$, the spatial 't Hooft loop exhibits a dual string tension, which vanishes at $T_c$ with 3D Ising-like critical exponent.

Figures (5)

• Figure 1: Partition function $Z_k/Z_0$ versus $k$. Incrementing $k$ always increase by $1$ the area of the 't Hooft loop, but only changes its perimeter by $\mp 2$ if $k = 0$ or $1$ mod(10) respectively. $Z_k$ is clearly sensitive to changes of perimeter but not of area.
• Figure 2: Free energy of a static pair of center monopoles as a function of their separation, at temperature $T < T_c$. The scaling behaviour of the data is mediocre. The curve shows a Yukawa potential with screening mass $2$ GeV.
• Figure 3: Free energy of a static pair of center monopoles as a function of their separation at temperature $T > T_c$. The spatial 't Hooft loop shows a dual string tension; the temporal 't Hooft loop shows a screening mass which increases with $T$.
• Figure 4: Screening mass as a function of temperature, both in units of $T_c$, as extracted from spatial (top) or temporal (bottom) 't Hooft loops. Below $T_c$ both coincide. The arrow gives the mass of the scalar glueball at $T=0$.
• Figure 5: Dual string tension, in units of $T_c^2$, as a function of the reduced temperature $t$. The straight line is a power law fit to $t < 1$. The fitted exponent is $1.32(6)$, to be compared with $2 \nu \approx 1.26$ for the $3D$ Ising model. The curves show the perturbative result, to leading (upper) and next (lower) order.