Field theory models for tachyon and gauge field string dynamics

TL;DR

This paper develops a scalar field theory model with lump solutions that closely resemble string theory tachyon dynamics, including mass spectra and condensation behavior, and extends it to include gauge fields with massless modes.

Contribution

It introduces an  scalar field theory model with lump solutions mimicking string theory tachyon properties, including exact solutions and gauge field incorporation.

Findings

Lump spectrum has equally spaced infinite levels with no continuous spectrum.

Tensions of higher codimension lumps satisfy a specific ratio close to 1.08.

Massless gauge fields emerge on the lump due to gauge fixed couplings.

Abstract

In hep-th/0008227, the unstable lump solution of \phi^3 theory was shown to have a spectrum governed by the solvable Schroedinger equation with the \ell=3 reflectionless potential and was used as a model for tachyon condensation in string theory. In this paper we study in detail an \ell\to \infty scalar field theory model whose lump solution mimics remarkably the string theory setup: the original field theory tachyon and the lump tachyon have the same mass, the spectrum of the lump consists of equally spaced infinite levels, there is no continuous spectrum, and nothing survives after tachyon condensation. We also find exact solutions for lumps with codimension \ge 2, and show that that their tensions satisfy (1/(2\pi)) (T_p/ T_{p+1})=e/(\sqrt{2\pi}) \approx 1.08. We incorporate gauge fixed couplings to a U(1) gauge field which preserve solvability and result in massless gauge fields on the lump.