Two loop renormalization of the magnetic coupling in hot QCD

Abstract

Well above the critical temperature hot QCD is described by 3d electrostatic QCD with gauge coupling $g_E$ and Debye mass $m_E$. We integrate out the Debye scales to two loop accuracy and find for the gauge coupling in the resulting magnetostatic action $g_M^2=g_E^2(1-\frac{1}{48}\frac{g_E^{2}N}{\pi m_E}-\frac{17}{4608}(\frac{g_E^{2}N}{\pi m_E}{)}^2+O((\frac{g_E^{2}N}{\pi m_E}{)}^3))$.

Comments: 5 pages, 1 figure. Cosmetic changes. To be published in Phys. Lett. B