Abstract
Pure lattice gauge theory in two dimensions can be solved analytically, either with open or with periodic boundary conditions. The exact solution on the torus can be used as a test bed for Monte Carlo algorithms. First we study simple Abelian gauge models for which the calculation parallels the treatment of one-dimensional spin systems. The second part deals with non-Abelian theories on the torus for which we use character expansions and a recursion formula due to Migdal to calculate the free energy and the potential energy between a static quark–antiquark pair. Gauge theories in two dimensions are in the confined phase, and for weak coupling the string tension shows an exact Casimir scaling. Towards the end of this chapter we collect some facts on invariant group integration which are useful in strong coupling expansions, mean field approximations and exact solutions.
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Wipf, A. (2013). Two-Dimensional Lattice Gauge Theories and Group Integrals. In: Statistical Approach to Quantum Field Theory. Lecture Notes in Physics, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33105-3_14
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DOI: https://doi.org/10.1007/978-3-642-33105-3_14
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