D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes

TL;DR

This paper introduces a D-independent Mellin amplitude framework for conformal field theories, connecting them to dual resonance models and revealing universal structures in scalar amplitudes across dimensions.

Contribution

It presents a novel D-independent representation of conformal field theories using Mellin amplitudes linked to dual resonance models, emphasizing universal features and pole structures.

Findings

Mellin amplitudes depend on complex dimensions with linear constraints.

Fields with spin produce simple poles in scalar 4-point Mellin amplitudes.

The leading pole determines the structure of satellite poles.

Abstract

The Euklidean correlation functions and vacuum expectation values of products of field operators of some Lorentz spin and dimension are expressed through Mellin amplitudes which depend on complex dimensions subject to linear constraints. The constraints can be solved in terms of conserved momenta whose squares are given by the field dimensions, and related Mandelstam variables s. The Mellin amplitudes furnish a universal representation of conformal field theories without explicit reference to D. The costumary principles of quantum field theory plus conformal invariance and operator product expansions (OPE) say that the Mellin amplitudes are amplitudes of dual resonance models with exact duality and a form of factorization which follows from OPE. Fields in the OPE with spin l and dimension d produce simple poles in the scalar 4-point Mellin amplitude at s=d-l+2n, n=0,1,2,3... with polynomial residues. The leading pole determines the satellites n=1,2,3...