Efectos de Temperatura Finita y Curvatura en QCD y Modelos de Quarks Quirales

TL;DR

This paper develops a heat kernel method at finite temperature to analyze QCD and chiral quark models, revealing new insights into the Polyakov loop, effective actions, and lattice data correlations.

Contribution

It introduces a comprehensive heat kernel approach for finite temperature QCD and chiral models, addressing gauge invariance and lattice data consistency.

Findings

Polyakov loop appears as a gauge covariant operator at finite temperature

Effective actions of QCD are computed and dimensionally reduced

Lattice data for the Polyakov loop fit well with a simple inverse power temperature correction

Abstract

We develop the heat kernel method in the context of finite temperature quantum field theory. We compute the heat kernel expansion in the presence of general gauge and scalar fields which may be non Abelian and non stationary. The Polyakov loop appears at finite temperature as a new gauge covariant operator. We apply this method in the computation of the fully gauge invariant effective action of QCD in the regime of high temperature. It is obtained the dimensionally reduced effective action of QCD as well. In the context of chiral quark models, in particular the Nambu--Jona-Lasinio and the spectral quark model, we apply this method to compute the low-energy chiral Lagrangian at finite temperature. The coupling of the Polyakov loop with these models allows to solve some inconsistencies appearing in the standard treatment at finite temperature: generation of multi-quark states, large $N_c$ counting, etc. On the other hand, we show that recent available lattice data for the renormalized Polyakov loop above the deconfinement phase transition exhibit unequivocal inverse power temperature corrections driven by a dimension 2 gluon condensate. This simple ansatz provides a good overall description of the data throughout the deconfinement phase until near the critical temperature with just two parameters. Finally, we study several chiral quark models in the light of chiral perturbation theory in curved space-time. The low energy structure of the energy momentum tensor in these models with SU(3) flavor symmetry is analyzed in the presence of external gravitational fields.