MULTILOOP FREE-ENERGY OF THE HETEROTIC STRING NEAR THE HAGEDORN TEMPERATURE

For the heterotic string we compute the critical exponent of the multi-loop free energy F near the Hagedorn temperature TH. With d uncompactified dimensions we find in particular the two-loop critical behaviour F(2) ∼ (TH-T)(d-2)/2, in contrast to the one-loop (free string) result F(1) ∼ (TH - T)d/2. For d = 3, we correspondingly obtain a finite pressure but a diverging two-loop energy density at the Hagedorn temperature which would appear as a limiting temperature in this case. Cosmological consequences are studied. © 1990.