Correlation functions of Polyakov loops at tree level

Pisarski, Robert D.; Skokov, Vladimir V.

Correlation functions of Polyakov loops at tree level

Robert D. Pisarski
(
- Brookhaven and
- Brookhaven Natl. Lab.
)
,
Vladimir V. Skokov
(
- Western Michigan U.
)

Jan 27, 2015

23 pages

e-Print:

1501.06904 [hep-ph]

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Abstract: (arXiv)

We compute the correlation functions of Polyakov loops in

SU(N_c)

gauge theories by explicitly summing all diagrams at tree level in two special cases, for

N_c = 2

and

N_c = \infty

. When

N_c =2

we find the expected we find Coulomb-like behavior at short distances,

\sim 1/x

as the distance

x \rightarrow 0

. In the planar limit at

N_c = \infty

we find a weaker singularity,

\sim 1/\sqrt{x}

as

x \rightarrow 0

. In each case, at short distances the behavior of the correlation functions between two Polyakov loops, and the corresponding Wilson loop, are the same. We suggest that such non-Coulombic behavior is an artifact of the planar limit.

Note:

23 pages, 1 figure

11.10.Wx
Polyakov loop: correlation function
tree approximation
gauge field theory: SU(N)
Wilson loop
singularity
Coulomb

References(14)

Figures(1)

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