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

Richard C. Brower
Phys. Rev. D 6, 1655 – Published 15 September 1972
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Abstract

The dual model is generally factorized using Lorentz oscillators anμ with ghost (or negativenorm) states arising from the indefinite metric ([an0, an0]=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 Qμ, Pμ) 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(+)]=(nm)An+m(+)+2n3δn+m,0. Increasing the number of spatial oscillators (ani, i=1, , D1), 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=12αs+2) as proposed by Lovelace.

  • Received 12 May 1972

DOI:https://doi.org/10.1103/PhysRevD.6.1655

©1972 American Physical Society

Authors & Affiliations

Richard C. Brower

  • Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

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Issue

Vol. 6, Iss. 6 — 15 September 1972

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