Rate of cluster decomposition via Fermat-Steiner point

Alexander Avdoshkin, Lev Astrakhantsev, Anatoly Dymarsky*, Michael Smolkin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In quantum field theory with a mass gap correlation function between two spatially separated operators decays exponentially with the distance. This fundamental result immediately implies an exponential suppression of all higher point correlation functions, but the predicted exponent is not optimal. We argue that in a general quantum field theory the optimal suppression of a three-point function is determined by total distance from the operator locations to the Fermat-Steiner point. Similarly, for the higher point functions we conjecture the optimal exponent is determined by the solution of the Euclidean Steiner tree problem. We discuss how our results constrain operator spreading in relativistic theories.

Original languageAmerican English
Article number128
JournalJournal of High Energy Physics
Issue number4
StatePublished - 1 Apr 2019

Bibliographical note

Funding Information:
We thank Slava Rychkov and David Simmons-Duffin for discussions. This work is supported by the BSF grant 2016186. The work of LA is supported by the Russian Academic Excellence Project ‘5-100’. AD is grateful to KITP for hospitality, where this work has been completed. The research at KITP was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958.

Publisher Copyright:
© 2019, The Author(s).


  • Effective Field Theories
  • Field Theories in Higher Dimensions
  • Field Theories in Lower Dimensions
  • Renormalization Regularization and Renormalons


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