Condensation of Localized Tachyons and Spacetime Supersymmetry

Abstract
We consider condensation of localized closed string tachyons by examining the recent proposal of Harvey, Kutasov, Martinec, and Moore (HKMM). We first observe that the $g_{m cl}$ defined by HKMM does not reflect the space-time supersymmetry when the model has the supersymmetry (SUSY). Especially for ${f C}^2/{f Z}_N$ models, $g_{m cl}$ is highly peaked along the supersymmetric points in the space of orbifolds, which is an unsatisfactory property of the c-function of the renormalization group(RG)-flow. We give an alternative proposal for the tachyon potential in type II cases such that it has a valley along the supersymmetric points in the orbifold moduli space. A new definition predicts that the processes suggested by Adams, Polchinski, and Silverstein and argued to be forbidden by HKMM are in fact allowed.

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