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arXiv:1208.6449 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Operator product expansion convergence in conformal field theory

Duccio Pappadopulo, Slava Rychkov, Johnny Espin, Riccardo Rattazzi A

Published Nov 26, 2012• 265 citations
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Abstract

We clarify questions related to the convergence of the operator product expansion 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 $\ensuremath{\Delta}$ contribute to correlation functions at most $\mathrm{exp}(\ensuremath{-}a\ensuremath{\Delta})$. Here the constant $a>0$ depends on the positions of operator insertions and we compute it explicitly.

DOI
10.1103/physrevd.86.105043

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