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

Understand

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.