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We continue the study of model-independent constraints on the unitary conformal field theories (CFTs) in four dimensions, initiated in R. Rattazzi, V. S. Rychkov, E. Tonni, and A. Vichi, J. High Energy Phys. 12 (2008) 031. Our main result is an improved upper bound on the dimension of the leading scalar operator appearing in the operator product expansion (OPE) of two identical scalars of dimension d: ₃₃=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 conformal block decomposition. We also discuss possible applications to particle phenomenology and, via a 2D analogue, to string theory.
Rychkov et al. (Fri,) studied this question.
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