# Scaling and the continuum limit of gluoN_c plasmas

## TL;DR

This study examines the finite temperature phase transitions of SU(Nc) gauge theories with Nc=4, 6, 8, 10 at small lattice spacings, using two-loop renormalization group equations to approach the continuum limit.

## Contribution

It provides precise critical couplings for various Nc and assesses the accuracy of two-loop extrapolations to the continuum, highlighting the limitations when using Lambda_MSbar as a scale.

## Key findings

- First order phase transitions observed at small lattice spacings.
- Two-loop extrapolation achieves 1-2% accuracy for a ≤ 1/(8Tc).
- Uncertainties increase to 5-10% when using Lambda_MSbar as the scale.

## Abstract

We investigated the finite temperature (T) phase transition for SU(Nc) gauge theory with Nc=4, 6, 8 and 10 at lattice spacing, a, of 1/(6T) or less. We found that these theories have first order transitions at such small a. In many cases we were able to find the critical couplings with precision as good as a few parts in 10^4. We also investigated the use of two-loop renormalization group equations in extrapolating the lattice results to the continuum, thus fixing the temperature scale in units of the phase transition temperature, Tc. We found that when a \le 1/(8Tc) the two-loop extrapolation was accurate to about 1--2%. However, we found that trading Tc for the QCD scale, Lambda_MSbar, increases uncertainties significantly, to the level of about 5--10%.