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

TL;DR

This paper introduces a factorization method for the second functional derivative of the effective potential in fermionic theories, simplifying the calculation of renormalization group flows within the Local Potential Approximation, demonstrated on specific models.

Contribution

It presents a novel factorization approach for the second derivative of the effective potential, enabling easier computation of RG flows in fermionic theories within the LPA.

Findings

Applied to Gross-Neveu and Nambu--Jona-Lasinio models

Simplified evaluation of the Wetterich equation for fermions

Validated approach with explicit model examples

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.