# Saving Tachyons in Open String Theory

## TL;DR

This paper constructs a local field theory for open string tachyons, showing that tachyon condensation leads to mass generation and disappearance from low-energy spectra, aligning with string scattering amplitudes.

## Contribution

It introduces a local field theoretical action for open string tachyons incorporating cubic and quartic interactions consistent with string amplitudes.

## Key findings

- Tachyon field must be complex to match Veneziano amplitude.
- A quartic potential stabilizes the tachyon, enabling condensation.
- Tachyon and gauge fields become massive and decouple at low energies.

## Abstract

Using string scattering amplitudes of open bosonic string on a single $D$-brane, we construct a local field theoretical action for tachyon fields. Cubic local interactions between various particles, belonging to the particle spectrum of string may be directly followed from three-string scattering amplitude. These cubic local interactions may generate perturbative non-local four-particle interactions, which may contribute to four-string scattering amplitude. It was observed that tachyon field in open bosonic string theory must be represented by a complex field in order to reproduce the Veneziano amplitude, describing four-tachyon scattering. The Veneziano amplitude, expanded in terms of $s$-channel poles was compared with the four-tachyon scattering amplitudes in $s$-channel generated perturbatively and it was found that a quartic potential term is needed in the local field theoretical action, which describes open string theory effectively in the low energy regime. With this quartic term, the tachyon potential has a stable minimum point and the tachyon field may condensate. As a result, both tachyon and gauge fields become massive at Planck scale and completely disappear from the low energy particle spectrum.