Spectrum-Generating Algebra and No-Ghost Theorem for the Dual Model

The dual model is generally factorized using Lorentz oscillators aₙ^μ with ghost (or negativenorm) states arising from the indefinite metric ([aₙ⁰, aₙ^0]=-1). Here all ghost states are proven to decouple for unit Regge intercept (α₀=1) as a consequence of the Virasoro gauges (Lₙ). By reformulating vertices in light-cone variables and exploiting the local commutators (for Q^μ, P^μ) on the Koba-Nielson circle, the spectrum-generating algebra (Aₙⁱ, Aₙ⁽⁺⁾) is found that commutes with all the gauges Lₙ. All physical states are explicitly constructed. The noghost theorem follows from the remarkable isomorphism of the transverse generators Aₙⁱ ($i=1, 2$) of Del Giudice, Di Vecchia, and Fubini to the original oscillators √naₙⁱ, [Aₙⁱ, Aₘʲ]=nδᵢⱼδn+m,0, and the isomorphism (up to c numbers) of the longitudinal generators Aₙ⁽⁺⁾ with the conformal group generators Lₗ, [Aₙ⁽⁺⁾, Aₘ⁽⁺⁾]=(n-m)Aₙ₊ₘ⁽⁺⁾+2n³δn+m,0. Increasing the number of spatial oscillators (aₙⁱ, i=1, , D-1), one observes a critical dimension $D=26$. For $D>26$ ghosts appear, for $D<26$ there are no ghosts, and A₁⁽⁺⁾ gives the null states postulated by Brower and Thorn. But for $D=26$, all Aₙ⁽⁺⁾ correspond to null states, so that the second-order Pomeranchukon is precisely a Regge pole (αP=1/2α^'s+2) as proposed by Lovelace.