Universal Constraints on Conformal Operator Dimensions

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 ∆ of the leading scalar operator appearing in the OPE of two identical scalars of dimension d: φd × φd = 1 +O ∆ +... In the interval 1 < d < 1.7 this universal bound takes the form ∆ ≤ 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 con-formal block decomposition. We also discuss possible applications to particle phenomenology and, via a 2-D analogue, to string theory. ar X i