Critical exponents for higher-representation sources in 3D SU(3) gauge theory from CFT

TL;DR

This paper maps the representation theory of 3D SU(3) gauge theory to 2D conformal field theory, enabling precise predictions of critical exponents for Polyakov line correlators across various representations, validated by simulations.

Contribution

It establishes an exact correspondence between SU(3) representation fusion rules and 2D CFT fusion algebra, extending the Svetitsky-Yaffe conjecture to higher representations.

Findings

Predicted critical exponents match Monte Carlo results.

Fusion algebra mapping confirms universality class.

Extension of Svetitsky-Yaffe conjecture to higher representations.

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.