Universal Constraints on Conformal Operator Dimensions

TL;DR

This paper derives an improved, universal upper bound on the dimension of the leading scalar operator in 4D unitary conformal field theories, based on fundamental principles like unitarity and crossing symmetry.

Contribution

It provides a new, tighter upper bound on scalar operator dimensions in 4D CFTs, extending previous constraints and employing fundamental CFT principles.

Findings

Derived an explicit upper bound on scalar operator dimensions for 1<d<1.7.

The bound improves upon previous constraints, offering tighter restrictions.

Discussed potential implications for particle physics and string theory.

Abstract

We continue the study of model-independent constraints on the unitary Conformal Field Theories in 4-Dimensions, initiated in arXiv:0807.0004. Our main result is an improved upper bound on the dimension \Delta of the leading scalar operator appearing in the OPE of two identical scalars of dimension d. In the interval 1<d<1.7 this universal bound takes the form \Delta<2+0.7(d-1)^{1/2}+2.1(d-1)+0.43(d-1)^{3/2}. The proof is based on prime principles of CFT: unitarity, crossing symmetry, OPE, and conformal block decomposition. We also discuss possible applications to particle phenomenology and, via a 2-D analogue, to string theory.