Non-Gaussian fixed points in fermionic field theories without auxiliary Bose-fields

Abstract

The functional equation governing the renormalization flow of fermionic field theories is investigated in $d$ dimensions without introducing auxiliary Bose-fields on the example of the Gross-Neveu and the Nambu--Jona-Lasinio model. The UV safe fixed points and the eigenvectors of the renormalization group equations linearized around them are found in the local potential approximation. The results are compared carefully with those obtained with partial bosonisation. The results do not receive any correction in the next-to-leading order approximation of the gradient expansion of the effective action.

arXiv commentextended version to appear in EPJC, 15 pages, 4 figures, uses svjour3

References in corpus (26)

• Exact evolution equation for the effective potential
• The Exact Renormalisation Group and Approximate Solutions
• Optimised Renormalisation Group Flows
• Functional renormalization group approach to correlated fermion systems
• Renormalization Group Flow of Quantum Gravity in the Einstein-Hilbert Truncation
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Renormalization Flow of Bound States
• Effective Action for the Quark-Meson Model
• Four - Fermi Theories in Fewer Than Four Dimensions
• Asymptotic safety: a simple example
• Phase transition and critical behaviour of the d=3 Gross-Neveu model
• Critical Behaviour of the 3d Gross-Neveu and Higgs-Yukawa Models
• Critical exponents of the Gross-Neveu model from the effective average action
• Flow Equations without Mean Field Ambiguity
• Large N and the renormalization group
• UV fixed-point structure of the three-dimensional Thirring model
• Higgs Mass Bounds from Renormalization Flow for a Higgs-top-bottom model
• Higgs Mass Bounds from Renormalization Flow for a simple Yukawa model
• An asymptotic safety scenario for gauged chiral Higgs-Yukawa models
• Equation of state and coarse grained free energy for matrix models
• Analysis of the Wilsonian Effective Potentials in Dynamical Chiral Symmetry Breaking
• Critical behavior of supersymmetric O(N) models in the large-N limit
• Local potential approximation for the renormalization group flow of fermionic field theories
• Evolution equations for the effective four-quark interactions in QCD
• Non-ladder Extended Renormalization Group Analysis of the Dynamical Chiral Symmetry Breaking
• Solving the QCD non-perturbative flow equation as a partial differential equation and its application to the dynamical chiral symmetry breaking

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• Gentle introduction to rigorous Renormalization Group: a worked fermionic example
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