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This is my master thesis in theoretical high energy physics. I finished this work with my supervisor Prof.Semenoff and Dr.Karczmarek. We worked on Gross-Witten model in Large N gauge theory under t Hooft limit. I focus on the k-representation of the SU(N) gauge group in 2- dimensional lattice, where k means the number of quarks. Our goal is to further understand quark confinement in Large N Quantum Chromodynamics(QCD) model. Prof. Semenoff derived the Action for the k-symmetric representation using the Saddle-Point Approximation. I further derived the Action of the k-exterior representation and we found an interesting phase transition from de-confined phase to confined phase when the number k changes. In Gross-Witten model, there is a phase transition as the coupling constant changes. In our study, both the coupling constant and the k-number give the whole phase transition diagram.
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