The spatial string tension from the Field Correlator Method

TL;DR

This paper demonstrates that the Field Correlator Method accurately predicts the linear temperature dependence of the spatial string tension in QCD, aligning well with lattice data across a broad temperature range.

Contribution

The paper provides a numerical calculation of the spatial string tension using FCM across temperatures from T_c to 5 T_c, confirming its validity without additional parameters.

Findings

Good agreement with lattice data for $\sigma_s$

Validation of FCM in high-temperature QCD

Justification for using FCM in thermodynamics

Abstract

The phenomenon of the almost linear growth of the square root of spatial string tension $\sqrt{\sigma_s(T)}= c_{\sigma} g^2 T$ was found both in lattice and in theory, based on the Field Correlator Method (FCM). In the latter the string tension (both spatial and colorelectric) is expressed as an integral of the two gluon Green's function calculated with the same string tension: $\sigma= \int G^{(2g)}_{\sigma}$. This relation allows to check the selfconsistency of the theory. However at nonzero temperature $T$ in the two-gluon Green's function in the space-like region appear terms which create in $\sigma_s$ quadratic in T behavior. We calculate below in the paper the $\sigma_s$ numerically in the whole temperature region $T_c< T < 5 T_c$ using the FCM method and compare the results with lattice data finding a good agreement. This justifies the use of the FCM in the space-like region and in high T thermodynamics without extra parameters.