2012/08/31 by Duccio Pappadopulo, Slava Rychkov, Johnny Espin +1 · 2 citations
Mathematics · Physics and Astronomy · #cond-mat.stat-mech #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.86.105043
26 pages, 6 figures; v2: a clarifying note and two refs added; v3: note added concerning an extra constant factor in the main error estimate, misprint corrected
arxiv created 2015/06/12 · arxiv updated 2015/06/15
We clarify questions related to the convergence of the OPE and conformal block decomposition in unitary Conformal Field Theories (for any number of spacetime dimensions). In particular, we explain why these expansions are convergent in a finite region. We also show that the convergence is exponentially fast, in the sense that the operators of dimension above Delta contribute to correlation functions at most exp(-a Delta). Here the constant a>0 depends on the positions of operator insertions and we compute it explicitly.