The claim that ChPT topological susceptibility fluctuations are always non-interacting relies on a determinant that the paper's own equations show to be nonzero, and the slab sub-volume analysis contains further algebraic errors.
The determination of $\alpha_s$ by the ALPHA collaboration
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abstract
We review the ALPHA collaboration strategy for obtaining the QCD coupling at high scale. In the three-flavor effective theory it avoids the use of perturbation theory at $\alpha > 0.2$ and at the same time has the physical scales small compared to the cutoff $1/a$ in all stages of the computation. The result $\Lambda_\overline{MS}^{(3)}=332(14)$~MeV is translated to $\alpha_\overline{MS}(m_Z)=0.1179(10)(2)$ by use of (high order) perturbative relations between the effective theory couplings at the charm and beauty quark "thresholds". The error of this perturbative step is discussed and estimated as $0.0002$.
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A Fluctuation Theory of Topological Susceptibility
The claim that ChPT topological susceptibility fluctuations are always non-interacting relies on a determinant that the paper's own equations show to be nonzero, and the slab sub-volume analysis contains further algebraic errors.