Quasiopen string

The quasiopen string in D dimensions is defined by the Nambu-Goto action and the boundary conditions (x'+x)(σ/sub α/,tau) = V/sub α/(x'-x)(σ/sub α/,tau), where σ = σ1 and σ2 denote the ends of the string, x'equivalentpartialx/partialσ, and the V/sub α/ (α = 1,2) are real symmetric orthogonal matrices. (The usual open string corresponds to V1 = V2 = -1.) We impose Poincare invariance in d dimensions, d<D. Classically this requires (V/sub α/)/sub jk/ = -δ/sub jk/ for j,kelement of Poincare sector and (V/sub α/)/sub jk/ = 0 if only one of j,k belongs to the Poincare sector. Further quantization gives D = 26 and a mass spectrum with a ground-state mass squared M/sub G/ 2 = -(1- summation/sub i/chemical bondtheta/sub i/chemical bond(1-chemical bondtheTa/sub I/chemical bond)/4)/α', where chemical bondtheta/sub i/chemical bond≤(1/2), exp(2iπtheta/sub i/) are the eigenvalues of V2V1, and α' is the slope parameter in the string action. A choice of theta/sub i/ giving a tachyon-free spectrum is thus possible if d≤10