OPE Convergence in Conformal Field Theory
High Energy Physics - Theory
2015-06-15 v3 Statistical Mechanics
Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.1208.6449,
title = {OPE Convergence in Conformal Field Theory},
author = {Duccio Pappadopulo and Slava Rychkov and Johnny Espin and Riccardo Rattazzi},
journal= {arXiv preprint arXiv:1208.6449},
year = {2015}
}
Comments
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