Conformal gauge-Yukawa theories away from four dimensions

  • Alessandro Codello
  • Kasper Langæble
  • Daniel F. Litim
  • Francesco Sannino
Open Access
Regular Article - Theoretical Physics


We present the phase diagram and associated fixed points for a wide class of Gauge-Yukawa theories in d = 4 + ϵ dimensions. The theories we investigate involve non-abelian gauge fields, fermions and scalars in the Veneziano-Witten limit. The analysis is performed in steps, we start with QCD d and then we add Yukawa interactions and scalars which we study at next-to- and next-to-next-to-leading order. Interacting infrared fixed points naturally emerge in dimensions lower than four while ultraviolet ones appear above four. We also analyse the stability of the scalar potential for the discovered fixed points. We argue for a very rich phase diagram in three dimensions while in dimensions higher than four certain Gauge-Yukawa theories are ultraviolet complete because of the emergence of an asymptotically safe fixed point.


Field Theories in Higher Dimensions Field Theories in Lower Dimensions Renormalization Group 


Open Access

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Alessandro Codello
    • 1
  • Kasper Langæble
    • 1
  • Daniel F. Litim
    • 2
  • Francesco Sannino
    • 1
    • 3
  1. 1.CP3-Origins, University of Southern DenmarkOdenseDenmark
  2. 2.Department of Physics and AstronomyUniversity of SussexBrightonU.K.
  3. 3.Danish Institute for Advanced Study, Danish IASUniversity of Southern DenmarkOdenseDenmark

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