Temperature Dependence of Electric and Magnetic Gluon Condensates

Abstract

The contribution of Lorentz non-scalar operators to finite temperature correlation functions is discussed. Using the local duality approach for the one-pion matrix element of a product of two vector currents, the temperature dependence of the average gluonic stress tensor is estimated in the chiral limit to be $\langle{\bf E}^2 +{\bf B}^2\rangle_{T}=\frac{\pi^2}{10}bT^4$. At a normalization point $\mu=0.5$ GeV we obtain $b\approx 1.1$. Together with the known temperature dependence of the Lorentz scalar gluon condensate we are able to infer $\langle{\bf E}^2\rangle_T$ and $\langle{\bf B}^2\rangle_T$ separately in the low-temperature hadronic phase.