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

The dual model is generally factorized using Lorentz oscillators a₍^ with ghost (or negativenorm) states arising from the indefinite metric (a₍^0, a₍^0=-1). Here all ghost states are proven to decouple for unit Regge intercept (₀=1) as a consequence of the Virasoro gauges (L₍). By reformulating vertices in light-cone variables and exploiting the local commutators (for Q^, P^) on the Koba-Nielson circle, the spectrum-generating algebra (A₍^i, A₍^ (+) ) is found that commutes with all the gauges L₍. All physical states are explicitly constructed. The noghost theorem follows from the remarkable isomorphism of the transverse generators A₍^i (i=1, 2) of Del Giudice, Di Vecchia, and Fubini to the original oscillators na₍^i, A₍^i, A₌^j=n₈₉₍+₌, ₀, and the isomorphism (up to c numbers) of the longitudinal generators A₍^ (+) with the conformal group generators L₋, A₍^ (+), A₌^ (+) = (n-m) A₍+₌^ (+) +2n^3₍+₌, ₀. Increasing the number of spatial oscillators (a₍^i, 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 A₍^ (+) correspond to null states, so that the second-order Pomeranchukon is precisely a Regge pole (₏=12^'s+2) as proposed by Lovelace.