Local potential approximation for the renormalization group flow of fermionic field theories

Abstract

The second functional derivative of the effective potential of pure fermionic field theories is rewritten in a factorized form which facilitates the evaluation of the renormalisation flow rate of the effective action in the Wetterich equation. It is applied to the Local Potential Approximation in cases, when the effective potential depends on scalar composites built from the fermions. The procedure is demonstrated explicitly on the example of the $N_f$-flavor Gross-Neveu model and the one-flavor chiral Nambu--Jona-Lasinio model.

16 pages, title changed, typos corrected, version published in PRD

References in corpus (11)

• Exact evolution equation for the effective potential
• The phase structure of the Polyakov--quark-meson model beyond mean field
• Susceptibilities near the QCD (tri)critical point
• Asymptotic safety: a simple example
• UV fixed-point structure of the three-dimensional Thirring model
• Critical behavior of the (2+1)-dimensional Thirring model
• Introduction to the nonequilibrium functional renormalization group
• Analytic continuation of functional renormalization group equations
• Renormalization Group Study of Magnetic Catalysis in the 3d Gross-Neveu Model
• Many-flavor Phase Diagram of the (2+1)d Gross-Neveu Model at Finite Temperature
• Renormalization of 2PI resummation: a renormalization scheme approach

Cited by in corpus (18)

• Aspects of asymptotic safety for quantum gravity
• Ising and Gross-Neveu model in next-to-leading order
• Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• Fixed points and the spontaneous breaking of scale invariance
• Critical $O(N)$ models in the complex field plane
• Asymptotic safety of scalar field theories
• Non-Gaussian fixed points in fermionic field theories without auxiliary Bose-fields
• Phase structure of NJL model with weak renormalization group
• Momentum dependence of quantum critical Dirac systems
• Disorder-driven quantum transition in relativistic semimetals: functional renormalization via the porous medium equation
• Line of Fixed Points in Gross-Neveu Theories
• Scalar mass stability bound in a simple Yukawa-theory from renormalisation group equations
• Critical Fermions with Spontaneously Broken Scale Symmetry
• Field dependence of the Yukawa coupling in the three flavor quark-meson model
• Scale symmetry breaking and generation of mass at quantum critical points
• Pseudo-Goldstone excitations in chiral Yukawa-theories with quadratic explicit symmetry breaking
• Fermion Mass Generation without Symmetry Breaking