Field theory models for tachyon and gauge field string dynamics

In hep-th/0008227, the unstable lump solution of phi (3) theory was shown t o have a spectrum governed by the solvable Schroedinger equation with the l = 3 reflectionless potential and was used as a model for tachyon condensat ion in string theory. In this paper we study in detail an l --> infinity sc alar field theory model whose lump solution mimics remarkably the string th eory setup: the original field theory tachyon and the lump tachyon have the same mass, the spectrum of the lump consists of equally spaced infinite le vels, there is no continuous spectrum, and nothing survives after tachyon c ondensation. We also find exact solutions for lumps with codimension greate r than or equal to 2, and show that that their tensions satisfy 1/2 pi T-p/ Tp+1 = e/root<(2<pi>)over bar> approximate to 1.08 We incorporate gauge fix ed couplings to a U(1) gauge field which preserve solvability and result in massless gauge fields on the lump.