QFT in AdS instead of LSZ

TL;DR

This paper demonstrates that quantum field theory in Anti-de Sitter space can reproduce key flat-space quantum field theory results, such as dispersion relations and unitarity bounds, offering an alternative to the LSZ framework.

Contribution

It establishes a rigorous connection between boundary correlators in AdS and flat-space S-matrix elements, deriving fundamental QFT properties without LSZ axioms.

Findings

S-matrix in AdS satisfies dispersion relations

Unitarity conditions are upheld in the flat-space limit

Froissart-Martin bound is derived from AdS QFT

Abstract

The boundary correlation functions for a QFT in a fixed AdS background should reduce to S-matrix elements in the flat-space limit. We consider this procedure in detail for four-point functions. With minimal assumptions we rigorously show that the resulting S-matrix element obeys a dispersion relation, the non-linear unitarity conditions, and the Froissart-Martin bound. QFT in AdS thus provides an alternative route to fundamental QFT results that normally rely on the LSZ axioms.