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Strong coupling expansion for Yang-Mills theory at finite temperature

Presenter: Jens Langelage — University of Münster

J. Langelage, G. Münster, O. Philipsen

Euclidean strong coupling expansion of the partition function is applied to lattice Yang-Mills theory at finite temperature, i.e. for lattices with a compactified temporal direction. The expansions have a finite radius of convergence and thus are valid only for β<βc (T<Tc). We have calculated the first few orders of such expansions for the free energy density as well as the screening-masses for the gauge groups SU(2) and SU(3). The resulting free energy series can be summed up and corresponds to a glueball gas, consisting of the lowest mass glueballs up to the calculated order. Our result can be used to fix the lower integration constant for Monte Carlo calculations of the thermodynamic pressure via the integral method, and shows from first principles that in the confined phase this constant is indeed exponentially small. Similarly, our results also explain the low sensitivity of screening masses to temperature below Tc, as observed in Monte Carlo simulations. Possibilities and difficulties in extracting βc from the series are discussed.