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Journal of High Energy Physics

, 2012:112 | Cite as

Limit cycles in four dimensions

  • Jean-François Fortin
  • Benjamín Grinstein
  • Andreas Stergiou
Article

Abstract

We present an example of a limit cycle, i.e., a recurrent flow-line of the beta-function vector field, in a unitary four-dimensional gauge theory. We thus prove that beta functions of four-dimensional gauge theories do not produce gradient flows. The limit cycle is established in perturbation theory with a three-loop calculation which we describe in detail.

Keywords

Conformal and W Symmetry Space-Time Symmetries Renormalization Group 

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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Jean-François Fortin
    • 1
  • Benjamín Grinstein
    • 1
  • Andreas Stergiou
    • 1
  1. 1.Department of PhysicsUniversity of CaliforniaSan Diego, La JollaU.S.A

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