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Vacuum structure and thermodynamics of two dimensional guage theories coupled to matter Paniak, Lori Dean


The physics of two-dimensional Yang-Mills theories both with and without heavy, static matter is investigated. In particular, we focus on the relationship of these systems to the mathematical structures of Lie group theory. From this point of view explicit calculations of the vacuum structure and thermodynamics of finite N SU(N) gauge theory with adjoint representation matter are carried out. The limit N → ∞ of these systems is also constructed, making connection with the well-known formalism of unitary matrix models. An example of adjoint and fundamental matter interacting via SU(N) gauge fields is considered explicitly and shown to have non-trivial phase structure which is qualitatively similar to what is expected to arise in higher dimensional gauge theories. This phase structure is interpreted in terms of group theoretic quantities. Finally, the case of fundamental representation matter interacting via SU(N) fields and confined to a one-dimensional box is examined. The formalism for detailed exploration of this system is developed and used to show that there is a phase transition as a function of particle density and size of the box. The consequences of this observation for a string theory interpretation of a gas of Wilson loops on the two-dimensional space-time sphere are briefly discussed.

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