# Phase structure and propagators at nonvanishing temperature for QCD and QCD-like theories

## TL;DR

This paper studies the phase structure and propagators of QCD and QCD-like theories at non-zero temperature using Dyson-Schwinger equations, comparing different gauge groups to test the universality of truncation schemes.

## Contribution

It demonstrates the universality of Dyson-Schwinger truncation schemes across different gauge groups by calculating propagators and phase transitions in $SU(2)$ and $G_2$ theories.

## Key findings

- Reproduces expected confinement/deconfinement and chiral transition types.
- Shows similar responses of different theories to quark-gluon vertex modifications.
- Provides benchmarks for functional equation calculations using lattice results.

## Abstract

We investigate the universality of truncation schemes for Dyson-Schwinger equations developed for quantum chromodynamics in theories which differ from quantum chromodynamics only in the gauge group. Our specific choices are the gauge groups $SU(2)$ and $G_2$, for which lattice calculations at nonvanishing chemical potential are possible. Thus, corresponding calculations can provide benchmarks for testing calculations with functional equations. We calculate the quark and gluon propagators and determine the chiral and dual chiral condensates at vanishing density to determine the confinement/deconfinement and chiral transitions, respectively. We can reproduce the expected type of transitions in the quenched and unquenched cases. In general, all three theories react very similarly to modifications of the employed model for the quark-gluon vertex.