PUB - Publikationen an der Universität Bielefeld

Lattice methods are the essential tool to study QCD in its non-perturbative framework. At finite baryon densities, Monte Carlo simulations are most severely hindered by the sign problem. Thus, a finite density analysis of thermodynamic observables is limited, and the exploration of the QCD phase diagram via lattice QCD requires new ideas to tackle the sign problem.

Within the strong coupling limit of lattice QCD (SC-LQCD), a dual formulation is known which suffers only from a mild sign problem, allowing studies at finite baryon densities. Moreover, the continuous time framework is employed, which exhibits many assets compared to standard discrete time analysis such as a faster sampling of configurations, the avoidance of extrapolations in N τ as well as a smoother treatment of observables on anisotropic lattices. On top of that, its feature of having static baryons removes the sign problem completely.

The measurement of the critical temperature T c at µ B = 0 or the determination of physical quantities such as the pion decay constant F π directly in the continuous time limit significantly removes uncertainties due to extrapolations in discrete time studies. The featured continuous time algorithm allows for a straightforward study of temporal correlators at zero and finite baryon density. Pole masses are extracted using correlated fits and the temperature dependence is analyzed. A Taylor expansion in the pressure allows to compare the finite density phase transition with the radius of convergence. The temperature dependence of Taylor coefficients is inspected and the pressure from finite density Monte Carlo simulations is reconstructed.

The continuous time limit within the SC-LQCD framework turns out to be highly promising for future projects such as studies with multiple flavors, at finite quark masses as well as at finite gauge coupling. Within the scope of this thesis, evidence is provided that the continuous time limit is well defined and suited to study QCD thermodynamics. This is illustrated with various applications.