Effective actions for finite temperature Lattice Gauge Theories

Abstract

We consider a lattice gauge theory at finite temperature in ($d$+1) dimensions with the Wilson action and different couplings $β_t$ and $β_s$ for timelike and spacelike plaquettes. By using the character expansion and Schwinger-Dyson type equations we construct, order by order in $β_s$, an effective action for the Polyakov loops which is exact to all orders in $β_t$. As an example we construct the first non-trivial order in $β_s$ for the (3+1) dimensional SU(2) model and use this effective action to extract the deconfinement temperature of the model.