  Wilson loop elements on torus are introduced into the partition function of
open strings as Polyakov's path integral at one-loop level. Mass spectra from
compactification and expected symmetry breaking are illustrated by choosing the
correct weight for the contributions from annulus and M\"obius strip. We show
that Jacobi's imaginary transformation connects the mass spectra with the
Wilson loops. The application to thermopartition function and cosmological
implications are briefly discussed.
