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linear Regge trajectories: 

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Soon afterward Virasoro [316] published an alternative form with full s , t , and u symmetry: 

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There were N -particle generalizations of these formulae, but most surprisingly they were found to be factorizable into a spectrum of single particle states of an infinite number of harmonic oscillators { α µ $_{m}$} , m = 1 , 2 , . . . . This suggested a tantalizing interpretation: these were not just phenomenological fitting func- tions but rather a tree approximation of a full-fledged quantum field theory. 

Unfortunately the Lorentz transformation properties of these operators im- plied the existence of negative norm states. By imposing algebraic constraints, now named after him, on the oscillator operators Virasoro removed these states [317]. Solving one problem led to another, though: this algebra implied that the leading trajectory associated with Eq. (2.13) had an intercept at α (0) = 1, which meant in turn that in addition to a massless vector the theory admit- ted a tachyonic ground state as well. Additionally, unitarity required not the usual d = 4 dimensions of hadronic physics but rather d = 26. Finally the 

