On Effective Actions for the Bosonic Tachyon

TL;DR

This paper derives an effective action for bosonic tachyons near the D-brane, analyzing their dynamics and energy conservation, revealing different pressure behaviors depending on the tachyon's potential side.

Contribution

It extends previous work to the bosonic case, providing a one-derivative effective action applicable near rolling tachyons with bounded energy.

Findings

Energy is conserved for tachyons rolling down the potential

Pressure decreases exponentially for well-behaved tachyons

Pressure blows up in finite time for tachyons on the wrong side

Abstract

We extend the analysis of hep-th/0304045 to the bosonic case and find the one-derivative effective action valid in the vicinity of rolling tachyons with an energy not larger than that of the original D-brane. For on-shell tachyons rolling down the well-behaved side of the potential in this theory, the energy is conserved and the pressure eventually decreases exponentially. For tachyons rolling down the ''wrong'' side, the pressure instead blows up in a finite time.