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

TL;DR

This paper investigates the instability mechanisms of certain string theory backgrounds, showing how they decay via tachyon condensation or semiclassical processes depending on the size of a compact dimension, linking tachyonic and semiclassical instabilities.

Contribution

It demonstrates the connection between tachyonic and semiclassical instabilities in string theory backgrounds and provides a concrete example of spacetime annihilation through non-localized tachyon condensation.

Findings

Decay via tachyon condensation when circle is small

Decay via semiclassical instanton when circle is large

Duality relates the two decay mechanisms at critical size

Abstract

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.