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## Phase transitions in lattice gauge theories: From the numerical sign problem to machine learning

Scherzer, Manuel

Lattice simulations of Quantum chromodynamics (QCD) are an important tool of modern quantum field theory. They provide high precision results from first principle computations and as such allow for comparison between experiment and theory. At finite baryon density, such simulations are no longer possible due to the numerical sign problem which occurs when the action of the theory becomes complex, leading to integrals over highly oscillatory functions. We investigate two approaches to solve this problem. We employ complex Langevin method, which is a complexified stochastic process and investigate its properties. We apply it to QCD in a region where other methods are unreliable, we go up to $\mu/T_c\approx 5$. We finally investigate its applicability for SU(2) real-time simulations. We also investigate the Lefschetz Thimble method, which solves the sign problem by deforming the manifold of integration, such that there is no more oscillatory behavior. We discuss aspects of the method in simple models and develop algorithms for higher dimensions.\\ Finally, we apply neural networks to lattice simulation data and use them to extract the order parameter for the phase transition in the Ising model and SU(2) gauge theory. Thus, we uncover what the neural network learns.