The quasiopen string

Abstract

The quasiopen string in D dimensions is defined by the Nambu-Goto action and the boundary conditions (x'+x)(σ_α,τ)=V_α(x'-x) (σ_α,τ), where σ=σ₁ and σ₂ denote the ends of the string, x'≡∂x/∂σ, and the V_α (α=1,2) are real symmetric orthogonal matrices. (The usual open string corresponds to V₁=V₂=−1.) We impose Poincaré invariance in d dimensions, d<D. Classically this requires (V_α)_jk=−δ_jk for j,k ∈ Poincaré sector and (V_α)_jk=0 if only one of j,k belongs to the Poincaré sector. Further quantization gives D=26 and a mass spectrum with a ground-state mass squared M_G²=−(1−J_i||theta_i||(1-||theTa_I||)/4)/α', where ||theta_i||≤(½), exp(2iπtheta_i) are the eigenvalues of V₂V₁, and α' is the slope parameter in the string action. A choice of theta_i giving a tachyon-free spectrum is thus possible if d≤10.