Rigorous Limits on the Interaction Strength in Quantum Field Theory

TL;DR

This paper establishes universal upper bounds on OPE coefficients in 4D Conformal Field Theories using conformal bootstrap techniques, with implications for particle physics experiments like the LHC.

Contribution

It provides the first model-independent bounds on OPE coefficients in 4D CFTs, derived through conformal bootstrap methods.

Findings

OPE coefficients are bounded by approximately 10(d-1) for 1<d<1.7.

The bounds constrain unparticle self-interaction cross sections at the LHC.

The method is based on conformal block decomposition and crossing symmetry.

Abstract

We derive model-independent, universal upper bounds on the Operator Product Expansion (OPE) coefficients in unitary 4-dimensional Conformal Field Theories. The method uses the conformal block decomposition and the crossing symmetry constraint of the 4-point function. In particular, the OPE coefficient of three identical dimension $d$ scalar primaries is found to be bounded by ~ 10(d-1) for 1<d<1.7. This puts strong limits on unparticle self-interaction cross sections at the LHC.