Abstract
We establish an exact mapping between the multiplication table of the irreducible representations of SU(3) and the fusion algebra of the two-dimensional conformal field theory in the same universality class of 3D SU(3) gauge theory at the deconfining point. In this way the Svetitsky-Yaffe conjecture on the critical behaviour of Polyakov lines in the fundamental representation naturally extends to whatever representation one considers. As a consequence, the critical exponents of the correlators of these Polyakov lines are determined. Monte Carlo simulations with sources in the symmetric two-index representation, combined with finite-size scaling analysis, compare very favourably with these predictions.
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