The SU(3) twisted gradient flow strong coupling without topological freezing

We investigate the role of topology on the latticedetermination of the SU(3)strong coupling renormalized viagradient flow. To deal with the topological freezing of stan-dard local algorithms, the definition of the coupling is usuallyprojected onto the zero topological sector. However, it is notobvious that this definition is not biased by the loss of ergod-icity. We instead avoid the topological freezing using a novelalgorithm, the Parallel Tempering on Boundary Conditions.The comparison with a standard algorithm shows that, evenin the case where the latter is severely frozen, one obtainsthe same projected coupling. Moreover, we show that thetwo definitions of the coupling, projected and non-projected,lead to the same flow of the renormalization scale. Our resultsimply that projecting the coupling does not affect the deter-mination of the dynamically-generated scale of the theory Lambda,as obtained through the step-scaling method.