Effective Lagrangian for the Polyakov line on a lattice
Dmitri Diakonov, Victor Petrov, Hans-Peter Schadler, Christof, Gattringer
TL;DR
This paper develops a lattice-based method for calculating the effective Lagrangian of the Polyakov line, revealing a new ultraviolet divergence that clarifies discrepancies between lattice and perturbative results.
Contribution
It introduces a mean field approximation approach to compute the effective potential and identifies a novel divergence affecting lattice and perturbative comparisons.
Findings
Effective potential matches lattice simulations at high temperatures.
Discovered a new ultraviolet divergence from longitudinal gluons.
Explains discrepancies between lattice results and perturbative calculations.
Abstract
We formulate a method for computing the effective Lagrangian of the Polyakov line on the lattice. Using mean field approximation we calculate the effective potential for high temperatures. The result agrees with recent lattice simulations. We reveal a new type of ultraviolet divergence (coming from longitudinal gluons) which dominates the effective potential and explains the discrepancy of the lattice simulations and standard perturbative calculations performed in covariant gauges.
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