D-dimensional Conformal Field Theories with anomalous dimensions as Dual Resonance Models

TL;DR

This paper establishes an exact correspondence between D-dimensional conformal field theories with anomalous dimensions and dual resonance models in possibly different dimensions, highlighting duality, crossing symmetry, and the role of Mellin amplitudes.

Contribution

It reveals a novel duality between conformal field theories and resonance models, extending the understanding of Mellin amplitudes and their properties across dimensions.

Findings

Mellin amplitudes exhibit exact duality and crossing symmetry.

Leading pole positions relate to operator dimensions in OPE.

Dimensional reduction connects to Anti de Sitter space.

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 analog of scattering amplitudes are called Mellin amplitudes; they depend on complex variables which substitute for the Mandelstam variables on which scattering amplitudes depend. The Mellin amplitudes satisfy exact duality - i.e. meromorphy 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 positions of the leading poles are given by the dimensions of fields in the OPE; their residues depend on D and determine satellites. Dimensional reduction and induction D goes to D-1 and D+1 are discussed. Dimensional reduction leads to the appearence of Anti de Sitter space.