Abstract. An exact correspondence is pointed out between conformal field theories in D-dimensions and dual resonance models in D' dimensions, where D' may differ from D. Dual resonance models, pioneered by Veneziano, were forerunners of string theory. The analogs of scattering amplitudes in dual resonance models are called Mellin amplitudes; they depend on complex variables s_ij which substitute for the Mandelstam variables on which scattering amplitudes depend. The Mellin amplitudes satisfy exact duality - i.e. meromorphy in s_ij with simple poles in single variables, and crossing symmetry - and an appropriate form of factorization which is implied by operator product expansions (OPE). Duality is a D-independent property. The position of the leading poles in s₁₂ is given by the dimensions of fields in the OPE, but there are also satellites and the precise correspondence between fields in the OPE and the residues of these poles depends on D. Dimensional reduction and dimensional induction D → D ± 1 are discussed. Dimensional reduction leads to the appearance of Anti de Sitter space.

Full-text: PDF