Spatial String Tension at High Temperatures and Quantitative Tests of Dimensionally Reduced Effective Theories

We calculate the spatial string tension in 2+1 flavour QCD in $(3+1)$ dimensions within a temperature range of $[166\mathrm{M}\mathrm{e}\mathrm{V},1000\mathrm{M}\mathrm{e}\mathrm{V}]$ using spatial Wilson loops with HYP smearing. We use the Highly Improved Staggered Quark action for fermions and the tree-level Symanzik improved gauge action for gluons at two lattice spacings corresponding to temporal extents $N_{\tau }=8$ and $10$. We then compare our results with dimensionally reduced effective theories at high temperatures (EQCD and MQCD) to test the onset of dimensional reduction in QCD.