# Search for the IR fixed point in the twisted Polyakov loop scheme

## TL;DR

This study investigates the running coupling in the Twisted Polyakov Loop scheme through non-perturbative methods, confirming perturbative results in the UV and exploring potential IR fixed points in SU(3) Yang-Mills and Nf=12 QCD.

## Contribution

It introduces a non-perturbative approach to measure the running coupling in the TPL scheme and applies it to both pure Yang-Mills and Nf=12 QCD, exploring IR fixed points.

## Key findings

- Reproduces perturbative running coupling in the UV.
- Agrees with theoretical predictions in the IR.
- Preliminary results suggest possible IR fixed point in Nf=12 QCD.

## Abstract

We present a non-perturbative study of the running coupling constant in the Twisted Polyakov Loop (TPL) scheme. We investigate how the systematic and statistical errors can be controlled {\it via} a feasibility study in SU(3) pure Yang-Mills theory. We show that our method reproduces the perturbative determination of the running coupling in the UV. In addition, our numerical result agrees with the theoretical prediction of this coupling constant in the IR. We also present our preliminary results for $N_f=12$ QCD, where an IR fixed point may be present.