# Three dimensional finite temperature SU(3) gauge theory in the confined region and the string picture

## TL;DR

This study investigates the correlation of Polyakov loops in three-dimensional SU(3) gauge theory at finite temperature, comparing lattice results with the bosonic string model and analyzing critical behavior near the phase transition.

## Contribution

It provides lattice calculations of Polyakov loop correlations in 3D SU(3) gauge theory at finite temperature and compares them with string models, including analysis of critical properties.

## Key findings

- Good agreement with string model for T<0.7T_c
- Critical properties match 2D three-state Potts model
- Critical temperature ratio aligns with string model predictions

## Abstract

We determine the correlation between Polyakov loops in three dimensional SU(3) gauge theory in the confined region at finite temperature. For this purpose we perform lattice calculations for the number of steps in the temperature direction equal to six. This is expected to be in the scaling region of the lattice theory. We compare the results to the bosonic string model. The agreement is very good for temperatures T<0.7T_c, where T_c is the critical temperature. In the region 0.7T_c<T<T_c we enter the critical region, where the critical properties of the correlations are fixed by universality to be those of the two dimensional three state Potts model. Nevertheless, by calculating the critical lattice coupling, we show that the ratio of the critical temperature to the square root of the zero temperature string tension, where the latter is taken from the literature, remains very near to the string model prediction.