One-loop evolution of a rolling tachyon

We study the time evolution of the one-loop diagram in Sen's rolling tachyon background. We find that at least in the long cylinder case they grow rapidly at late time, due to the exponential growth of the timelike oscillator terms in the boundary state. This can also be interpreted as the virtual open string pair creation in the decaying brane. This behavior indicates a breakdown of this rolling tachyon solution at some point during the evolution. We also discuss the closed string emission from this one-loop diagram, and the evolution of a one-loop diagram connecting a decaying brane to a stable brane, which is responsible for the physical open string creation on the stable brane.