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

Abstract

We calculate the spatial string tension in 2+1 flavour QCD in $(3{+}1)$ dimensions within a temperature range of $[166\,\mathrm{MeV},\,1000\,\mathrm{MeV}]$ 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 $N_τ= 8$ 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.