Extended Data Figure 9: Topological susceptibility in the pure gauge theory.
From: Calculation of the axion mass based on high-temperature lattice quantum chromodynamics
The results shown are from an earlier direct simulation5 and from the novel fixed sector integral technique. Upper panel, the temperature dependence of decay exponent b; lower panel, temperature dependence of the topological susceptibility itself. Filled red and pink circles show the lattice results for the decay exponent on 8 × 323 and 8 × 643 lattices, respectively. The open circles show the topological susceptibility from the fixed sector integral technique. The green band refers to the result of ref. 5, the key shows the abbreviated arXiv preprint number. The black arrow indicates the Stefan–Boltzmann limit. We also show the result from the DIGA with blue bands, see, for example, ref. 33. To convert the result into units of Tc we used 
from ref. 15. The width of the DIGA prediction reflects the change of the renormalization scale from 1/2 πT to 2 πT. For the exponent b we see a good agreement for temperatures above ~4Tc, for smaller temperatures the lattice tends to give smaller values than the DIGA. In the case of the susceptibility, the DIGA underestimates the lattice result by about an order of magnitude, this has already been observed in ref. 5. The ratio at T = 2.4Tc is K = 11.1(2.6), where the error is dominated by the lattice calculation. Error bars, s.e.m.
