QUANTUM-FIELDS VERSUS STRINGS AT FINITE TEMPERATURE

We study some aspects of the relationship between the one-loop free energy of closed superstrings computed as a sum over the free energies of the quantum fields present in the string (the analog model) and the modular invariant expression of the same quantity. In particular, by getting a generalized duality relation for the integrand of the modular invariant expression for the free energy of closed superstrings and using a regularization procedure, we connect the contribution to the vacuum energy from the bosonic degrees of freedom in the analog model (one half of the total number) with the coefficient governing the high temperature behavior of the free energy. We also study the physical meaning of this regularization and the role played by the left-right constraint defining the physical fields in the light-cone gauge.