Sigma model approach to string theory effective actions with tachyons

TL;DR

This paper clarifies how the sigma model approach can derive effective actions for tachyons and gauge fields in string theory, resolving previous issues and ensuring consistency with string S-matrix results.

Contribution

It demonstrates that the renormalized partition function of the boundary sigma model yields a gauge-invariant effective action compatible with string S-matrix and beta functions, addressing longstanding problems.

Findings

Partition function Z(T,A) reproduces effective action consistent with string S-matrix.

Gauge-invariant definition of Z(T,A) in non-abelian NSR open string theory.

Derived actions for tachyon and massless modes in closed bosonic and NSR string theories.

Abstract

Motivated by recent discussions of actions for tachyon and vector fields related to tachyon condensation in open string theory we review and clarify some aspects of their derivation within sigma model approach. In particular, we demonstrate that the renormalized partition function $Z(T,A)$ of boundary sigma model gives the effective action for massless vectors which is consistent with string S-matrix and beta function, resolving an old problem with this suggestion in bosonic string case at the level of the leading $F^2 (dF)^2$ derivative corrections to Born-Infeld action. We give manifestly gauge invariant definition of $Z(T,A)$ in non-abelian NSR open string theory and check that its derivative reproduces the tachyon beta function in a particular scheme. We also discuss derivation of similar actions for tachyon and massless modes in closed bosonic and NSR (type 0) string theories.