DUALITY IN NONTRIVIALLY COMPACTIFIED HETEROTIC STRINGS

We study the implications of duality symmetry on the analyticity prope rties of the partition function as it depends upon the compactificatio n length. In order to obtain nontrivial compactifications, we give a p hysical prescription to get the Helmholtz free energy for any heteroti c string, supersymmetric or not. After proving that the free energy is always invariant under the duality transformation R --> alpha'/(2R) a nd getting the zero-temperature theory whose partition function corres ponds to the Helmholtz potential, we show that the self-dual point R0 = square-root alpha'/2 is a generic singularity like the Hagedorn one. The main difference between these two critical compactification radii is that the term producing the singularity at the self-dual point is finite for any R not-equal R0. We see that this behavior at R0 actuall y implies a loss of degrees of freedom below that point.