Abstract
We consider SU(N) gauge theories on a two-dimensional torus with finite area, . Let denote the Polyakov loop operator in the direction. Starting from the lattice gauge theory on the torus, we derive a formula for the continuum limit of as a function of the area of the torus where and are class functions. We show that there exists a class function for SU(2) such that for all finite area of the torus with the limit being unity as the area of the torus goes to infinity. Only the trivial representation contributes to as whereas all representations become equally important as .
- Received 12 March 2014
DOI:https://doi.org/10.1103/PhysRevD.89.085031
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