Abstract
The perturbative vacuum of type 0 string theory is unstable due to the existence of the closed string tachyon. This instability can be removed by ${\mathbf{S}}^{1}$ compactification with the twisted boundary condition for the tachyon field. We show that even in this situation unwrapped NS5-branes are unstable and decay to bubbles of nothing smoothly without tunneling any potential barrier. We discuss a relation between the closed string tachyon condensation and the instability of NS5-branes.
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