We build an EFT which accurately captures low energy physics of the chiral sector of QCD. When fitted to properties of pions at finite temperature obtained from lattice simulations of 2+1 flavour QCD, it accurately reproduces the crossover temperature seen in the simulations. Its predictions for other quantities are shown. The EFT can then be used for analytic continuation to real time. An interesting property of the continuation is demonstrated.
Gupta et al. (Mon,) studied this question.