Sigma model approach to string theory effective actions with tachyons

Motivated by recent discussions of actions for tachyon and vector fields re lated to tachyon condensation in open string theory we review and clarify s ome aspects of their derivation within the sigma model approach. In particu lar, we demonstrate that the renormalized partition function Z(T,A) of the boundary sigma model gives the effective action for massless vectors which is consistent with the string S-matrix and beta function, resolving an old problem with this suggestion in the bosonic string case at the level of the leading F-2(dF)(2) derivative corrections to Born-Infeld action. We give a manifestly gauge invariant definition of Z(T,A) in non-Abelian NSR open st ring theory and check that its derivative reproduces the tachyon beta funct ion in a particular scheme. We also discuss the derivation of similar actio ns for tachyon and massless modes in closed bosonic and NSR (type 0) string theories. In the bosonic case the tachyon potential has the structure -T(2 )e(-T), but it vanishes in the NSR string case. (C) 2001 American Institute of Physics.