Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-11-24
Phys.Rev.D70:034511,2004
Physics
High Energy Physics
High Energy Physics - Theory
24 pages, 7 figures; v2, 27 pages, 12 figures, extended discussion for clarity, results unchanged
Scientific paper
10.1103/PhysRevD.70.034511
We discuss how to extract renormalized from bare Polyakov loops in SU(N) lattice gauge theories at nonzero temperature in four spacetime dimensions. Single loops in an irreducible representation are multiplicatively renormalized without mixing, through a renormalization constant which depends upon both representation and temperature. The values of renormalized loops in the four lowest representations of SU(3) were measured numerically on small, coarse lattices. We find that in magnitude, condensates for the sextet and octet loops are approximately the square of the triplet loop. This agrees with a large $N$ expansion, where factorization implies that the expectation values of loops in adjoint and higher representations are just powers of fundamental and anti-fundamental loops. For three colors, numerically the corrections to the large $N$ relations are greatest for the sextet loop, $\leq 25%$; these represent corrections of $\sim 1/N$ for N=3. The values of the renormalized triplet loop can be described by an SU(3) matrix model, with an effective action dominated by the triplet loop. In several ways, the deconfining phase transition for N=3 appears to be like that in the $N=\infty$ matrix model of Gross and Witten.
Dumitru Adrian
Hatta Yoshitaka
Lenaghan Jonathan
Orginos Kostas
Pisarski Robert D.
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