Universal Constraints on Conformal Operator Dimensions

2009/05/31 by Vyacheslav S. Rychkov, Alessandro Vichi · 1 citation
Physics and Astronomy · #hep-th #hep-ph

paper · pdf · doi:10.1103/physrevd.80.045006

published as Phys.Rev.D80:045006,2009 · 14pp + 2 appendices v2: minor corrections; version to be published in PhysRev.D; numerical data files included in the source file

arxiv created 2009/07/09 · arxiv updated 2015/03/13

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 Δof 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 Δ<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.

Citations

• Bounding scalar operator dimensions in 4D CFT

Cited by

• Moduli Bounds from Spin-2 Sum Rules