Thermodynamical potential in compactified superstrings

An effective potential is calculated for an open and closed superstring in the M4xT6 background at nonzero temperature, where M4 is Minkowsky space and T6 is a 6-dimensional torus. For fermions along the fifth compactified dimension on the torus antiperiodic boundary conditions are chosen and in all remaining dimensions periodic boundary conditions are used. The effective potential is shown to be finite if the inverse temperature β>βcr= √8α'π2 and the raius of the fifth dimension R5>√2α'