Geodesic
Tachyon Effective Actions in String Theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 3, pp. 540-560

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We discuss the derivation of string effective actions for tachyons and massless modes within the sigma-model approach. We mostly consider the open string case, demonstrating that the renormalized partition function of the boundary sigma model gives the effective action for the massless vector and tachyon in the derivative expansion. We give a manifestly gauge-invariant definition of $Z(T,A)$ in the non-Abelian Neveu–Schwarz–Ramond (NSR) open string theory and verify that its derivative reproduces the tachyon beta function in a particular scheme. We also comment on the derivation of similar actions for tachyons and massless modes in the closed bosonic and the NSR string theories. 
@article{TMF_2001_128_3_a14,
     author = {A. A. Tseytlin},
     title = {Tachyon {Effective} {Actions} in {String} {Theory}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {540--560},
     publisher = {mathdoc},
     volume = {128},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_128_3_a14/}
}
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A. A. Tseytlin. Tachyon Effective Actions in String Theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 3, pp. 540-560. http://geodesic.mathdoc.fr/item/TMF_2001_128_3_a14/