2010/09/30 by David Poland, David Simmons-Duffin, David Simmons–Duffin
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Particle physics theoretical and experimental studies #hep-ph #hep-th
paper · pdf · doi:10.1007/jhep05(2011)017
published as JHEP 1105:017,2011 · 47 pages, 9 figures; V2: small corrections and clarifications
arxiv created 2011/04/27 · openalex publication_date 2011/05/01 · arxiv updated 2011/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive general bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N=1 superconformal field theories. In any CFT containing a scalar primary phi of dimension d we show that crossing symmetry of <phi phi phi phi> implies a completely general lower bound on the central charge c >= fc(d). Similarly, in CFTs containing a complex scalar charged under global symmetries, we bound a combination of symmetry current two-point function coefficients tauIJ and flavor charges. We extend these bounds to N=1 superconformal theories by deriving the superconformal block expansions for four-point functions of a chiral superfield Phi and its conjugate. In this case we derive bounds on the OPE coefficients of scalar operators appearing in the Phi x Phi* OPE, and show that there is an upper bound on the dimension of Phi* Phi when dim(Phi) is close to 1. We also present even more stringent bounds on c and tauIJ. In supersymmetric gauge theories believed to flow to superconformal fixed points one can use anomaly matching to explicitly check whether these bounds are satisfied.