Abstract
After a brief review of the necessary parts of the theory of the bosonic string, a consistent pp-wave background with constant dilaton and constant three-index antisymmetric field strength is introduced. In particular, the gravitational background is the plane wave with constant coefficients, and the antisymmetric field strength is chosen such that the worldsheet theory is both diff×Weyl invariant and stable. The one-loop closed bosonic string amplitude is evaluated and shown to be modular invariant. Then the free energy of a free closed string gas is calculated, modular invariance of it is proved, and the result is shown to be equivalent to the sum of free energies for the individual particle states.
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