THERMAL PARTITION FUNCTION OF NON-CRITICAL BOSONIC STRINGS

Abstract

The thermal free energy of free non-critical bosonic strings in a D-dimensional spacetime is examined. By integrating (or summing) over the Weyl freedom, the free energy and the one-loop vacuum amplitude are modular invariant for any D<26. Thus the (background) Weyl invariance is realized. In the case of L→∞, where L is the compactification radius of the Weyl mode, the physical spectrum circulating in the loop becomes continuous. A connection between this continuous spectrum and the unitarity of string perturbation theory is briefly mentioned.