On scale and conformal invariance in four dimensions

Anatoly Dymarsky, Zohar Komargodski, Adam Schwimmer, Stefan Theisen

Research output: Contribution to journalArticlepeer-review

60 Scopus citations


Abstract: We study the implications of scale invariance in four-dimensional quantum field theories. Imposing unitarity, we find that infinitely many matrix elements vanish in a suitable kinematical configuration. This vanishing is a nontrivial necessary condition for conformality. We provide an argument why this is expected to be a sufficient condition as well, thereby linking scale and conformal invariance in unitary theories. We also discuss possible exceptions to our argument.

Original languageEnglish
Article number171
JournalJournal of High Energy Physics
Issue number10
StatePublished - Oct 1 2015

Bibliographical note

Publisher Copyright:
© 2015, The Author(s).


  • Anomalies in Field and String Theories
  • Effective field theories
  • Renormalization Group
  • Space-Time Symmetries

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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