Closed-string Tachyon Condensation and On-shell Effective Action of Open-string Tachyons

We study how the effect of closed-string tachyon condensation can enter into the on-shell effective action of open-string tachyons, for bosonic case. We also consider the open-string one-loop quantum corrections to the action. We use sigma-model approach with boundary terms, and we utilize some results of boundary string field theory (BSFT) to define the on-shell effective action. We regard D-instanton-like objects with appropriate weight as closed-string tachyon tadpoles, and we insert them into the worldsheet to analyze the effect of closedstring tachyons. In general, such a D-instanton-like tadpole causes divergence as well as a diagram of open-string one-loop quantum correction does. However, it is already known that an appropriate choice of the weight cancels those divergences. We find this gives a natural choice of the weight of the closed-string tachyon tadpoles, which should be determined by some non-perturbative method rigorously. Using the method presented here, we obtain a finite correction to the on-shell effective action of open-string tachyons, at least at the one-loop level of openstrings. ∗[email protected]