Universal Constraints on Conformal Operator Dimensions

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.