S-matrix elements and off-shell tachyon action with non-abelian gauge symmetry

TL;DR

This paper proposes a unique non-abelian expansion for string theory tachyon S-matrix elements, analyzing their structure and gauge invariance, and compares results in bosonic and superstring theories to known effective actions.

Contribution

It introduces a prescription for expanding string tachyon S-matrix elements into a non-abelian gauge invariant action, clarifying the structure of couplings in both bosonic and superstring theories.

Findings

Superstring leading terms match the symmetrised trace of the tachyonic Born-Infeld action.

Bosonic theory includes additional gauge invariant couplings beyond the symmetrised trace.

The proposed expansion aligns with known effective actions in superstring theory.

Abstract

We propose that there is a unique expansion for the string theory S-matrix elements of tachyons that corresponds to non-abelian tachyon action. For those S-matrix elements which, in their expansion, there are the Feynman amplitudes resulting from the non-abelian kinetic term, we give a prescription on how to find the expansion. The gauge invariant action is an $\alpha'$ expanded action, and the tachyon mass $m$ which appears as coefficient of many different couplings, is arbitrary. We then analyze in details the S-matrix element of four tachyons and the S-matrix element of two tachyons and two gauge fields, in both bosonic and superstring theories, in favor of this proposal. In the superstring theory, the leading terms of the non-abelian gauge invariant couplings are in agreement with the symmetrised trace of the direct non-abelian generalization of the tachyonic Born-Infeld action in which the tachyon potential is consistent with $V(T)=e^{\pi\alpha' m^2T^2}$. In the bosonic theory, on the other hand, the leading terms are those appear in superstring case as well as some other gauge invariant couplings which spoils the symmetrised trace prescription. These latter terms are zero in the abelian case.