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 renormalization 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.

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

“…This fact hints at prospective efficient usage of the technique developed in [21] without the introduction of any scalar auxiliary field also in more complicated models.…”

“…It is natural to expect that the established characteristics of U (I ) is carried over also to the finite N f case. The derivation of the Wetterich equation for the effective action with x-dependent Fermi fields (ψ(x), ψ(x)) and their transposed doublers (ψ T (x),ψ T (x)) closely follows the steps presented in our previous publication [21]. We start with a form where the traces with respect to the bispinor and flavor indices have already been done:…”

“…(10) one finds an expression which depends only on the scalar invariant (ψ 0 ψ 0 ) and was given explicitly with optimized infrared regulator [32] in Eq. (31) of [21]. This equation is transformed in two steps into a form convenient for finding the fixed points and the scaling exponents characterizing the behavior of different operators in its neighborhood.…”

“…In Sect. 2 we reformulate the version of the Wetterich equation derived in [21] for the Gross-Neveu model in a space-dependent fermionic background. It is projected on a constant background in Sect.…”

Scalar mass stability bound in a simple Yukawa-theory from renormalization group equations

“…In earlier papers the super-trace was evaluated on a background exclusively consisting of a nonzero σ-condensate 14 , where Γ publications clear arguments were put forward 21,23 how the Grassmannian nature of the fermi fields is compatible with a coarse grained background where also nonzero…”