Tachyon effective actions in string theory

We discuss the derivation of string effective actions for tachyons and mass less modes within the sigma-model approach. We mostly consider the open str ing case, demonstrating that the renormalized partition function of the bou ndary sigma model gives the effective action for the massless vector and ta chyon in the derivative expansion. We give a manifestly gauge-invariant def inition of Z(T, A) in the non-Abelian Neveu-Schwarz-Ramond (NSR) open strin g theory and verify that its derivative reproduces the tachyon beta functio n in a particular scheme. We also comment on the derivation of similar acti ons for tachyons and massless modes in the closed bosonic and the NSR strin g theories.