Stable solitons in field theory models for tachyon condensation

Abstract

We study soliton solutions in scalar field theory with a variety of unbounded potentials. A subset of these potentials have Gaussian lump solutions and their fluctuation spectrum is governed by the harmonic oscillator problem. These lumps are unstable with one tachyonic mode. Soliton solutions in several other classes of potentials are stable and are of kink type. The problem of the stability of these solutions is related to a supersymmetric quantum mechanics problem. The fluctuation spectrum is not equispaced and does not contain any tachyonic mode. The lowest energy mode is the massless Goldstone mode which restores broken translation invariance.

Noncommutative Field Theories and (Super)string Field Theories

“…The second Sen's conjecture was also verified almost in all SFTs [238,239,240,241,242,243,244,245,246,247] and [248]. For superstrings the solution representing, for example, a decay non-BPS D9 → BPS D8 (D8) is a kink (anti-kink) solution.…”

A note on fermion and gauge couplings in field theory models for tachyon condensation

“…It is clear from the field redefinition (18) that Substituting this in (24), we find that the potential U(x) in the Schrödinger operator is the same as that for the scalar fluctuations about the kink solution obtained in [16]:…”

“…This paper is a continuation along the lines of investigation started in [16] where we studied soliton solutions for a class of scalar field theory models with potentials that are not bounded below. They correspond to odd values of a parameter n. In this paper we study the same for potentials that are bounded below, corresponding to even values of n.…”

“…We saw in [16] that this defines a supersymmetric (SUSY) quantum mechanics problem [18] with superpotential given by…”

Novel connection between lump-like structures and quantum mechanics

“…In particular, the lump-like structures which we will be studying in the current work may contribute to the formation of structures in the early Universe [1,15,16] and q-balls [17][18][19][20][21], vortons [22,23] and oscillons [24][25][26] in high energy physics. They can also be used to describe bright solitons in applications in optical fibers [27][28][29], tunneling effects in quantum mechanics [30], and to model tachyon condensation and lump solutions in string theory [31][32][33][34][35][36][37]. Since the lump-like structures are in general unstable, one can also use them to model dissipation, making contact with two interesting studies concerning the presence of dissipation in quantum gravity [38] and in classical mechanics [39], among other interesting possibilities.…”