Semi-localized instability of the Kaluza-Klein linear dilaton vacuum

The Kaluza-Klein linear dilaton background of the bosonic string and the Scherk-Schwarz linear dilaton background of the superstring are shown to be unstable to the decay of half of spacetime. The decay proceeds via a condensation of a semi-localized tachyon when the circle is smaller than a critical size, and via a semiclassical instanton process when the circle is larger than the critical size. At criticality the two pictures are related by a duality of the corresponding two-dimensional conformal field theories. This provides a concrete realization of the connection between tachyonic and semiclassical instabilities in closed string theory, and lends strong support to the idea that non-localized closed string tachyon condensation leads to the annihilation of spacetime.