Browsing by Author "Rajala, Aatu"
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Rajala, Aatu (2024)Color confinement, the inability for free quarks to exist at normal temperatures and densities, is one of the most important properties of Quantum Chromodynamics, the quantum field theory (QFT) of the strong interaction. A simple representation of confinement can be obtained by considering a static (i.e. infinitely massive) quarkantiquark pair. The potential of the pair contains a term linear with respect to the separation. Therefore, separating the pair would require infinite energy meaning that the quarks are confined. The static potential can be related to the expectation value of a QFT operator called the Wilson loop. In the nonperturbative large coupling regime lattice field theory can be applied to estimate expectation values of observables. The idea of lattice field theory is to replace continuous spacetime with a lattice, where the fields are defined on the sites and links. The discretization of spacetime allows evaluating path integrals numerically using Monte Carlo methods. An alternate way of computing the Wilson loop expectation value is provided by holographic duality. It is an equivalence between a QFT in fourdimensional flat spacetime and a higherdimensional theory of gravity in curved spacetime. The duality allows evaluation of hard, nonperturbative QFT calculations with easy classical computations on the gravity side. From the lattice data of the static potential, we can construct a holographic model that could produce those results in a process called bulk reconstruction. The constructed holographic model can then be used to compute other QFT quantities such as entanglement entropy. These quantities allow us to study confinement among other things. In this thesis, lattice field theory measurements of the static potential at different temperatures are presented. Then using a machine learning method, the corresponding holographic metrics are constructed from the lattice results. The lattice simulations have been done as a learning exercise and for the bulk reconstruction method, this thesis is a proof of concept, where no further computations are done using the constructed metrics. The lattice results are in good agreement with previous ones and the bulk reconstruction method seems to work as intended. In future works the method should be applied to a bigger dataset and other quantities should be computed with the constructed metrics.
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