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

TL;DR

This paper investigates non-Gaussian fixed points in fermionic field theories like Gross-Neveu and Nambu--Jona-Lasinio models without auxiliary bosonic fields, analyzing their renormalization group flows and fixed points.

Contribution

It demonstrates the existence of UV safe fixed points in fermionic theories without auxiliary fields and compares these results with partial bosonization approaches.

Findings

Identification of UV fixed points in fermionic models

Fixed points consistent across different approximation methods

No corrections in next-to-leading order gradient expansion

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.