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Real-time quantities like spectral functions and transport coefficients arecrucial for a proper understanding of the quark-gluon plasma created inrelativistic heavy-ion collisions. Their numerical computation is plagued by asevere sign problem inherent in the real-time formulation of lattice fieldtheories. In this letter, we present the first direct ab-initio computation ofunequal-time correlation functions in non-Abelian lattice gauge theory, whichare necessary to extract real-time quantities. We demonstrate non-trivialconsistency relations among correlators, time-translation invariance, andagreement with Monte-Carlo results for thermal equilibrium in 3+1 dimensions byemploying our stabilized complex Langevin method. Our work sets the stage toextract real-time observables in lattice gauge theory in a first-principlesreal-time framework.

Real-time correlators in 3+1D thermal lattice gauge theory