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Strongly Coupled Fermions in Odd Dimensions and the Running Cut-off Λd

One may observe that the fermionic U(N) Gross-Neveu model at imaginary chemical potential and finite temperature for odd d dimensions, in the strong coupling regime, by using the gap (saddle point) equation for the fermion condensate of the model. This equation describes the phase transitions from weak to strong coupling regime. It is pointed out that the higher odd dimensional gap equations are linear combinations of the lower dimensional equations in a way that as the dimension of the model increases the lower dimensions are weaker coupled but still in the strong coupling regime. Interestingly, at a specific value of the chemical potential, exactly in the middle of the thermal windows that separate the fermionic from the bosonic (condensed) state of the fermions, it is found that the mass of the fermion condensate for d = 3, 5, 7, 9. An anomaly occurs at the 5 dimensional theory where it is stronger coupled against other theories in higher dimensions and lower energy. The main idea of this work is that the cut-off Λ regulator for the UV divergent parts of the fermion mass saddle point equation, plays the role of a physical parameter that makes the separation of the odd dimensional fermionic theories according to how deep they are in the strong coupling regime. This idea is based on the identity of the asymptotic freedom of the Gross-Neveu model as a toy model for QCD.

Gross-Neveu, Strong Coupling, Cut-off

APA Style

Filothodoros, E. G. (2024). Strongly Coupled Fermions in Odd Dimensions and the Running Cut-off Λd. American Journal of Modern Physics, 13(1), 1-11.

ACS Style

Filothodoros, E. G. Strongly Coupled Fermions in Odd Dimensions and the Running Cut-off Λd. Am. J. Mod. Phys. 2024, 13(1), 1-11. doi: 10.11648/j.ajmp.20241301.11

AMA Style

Filothodoros EG. Strongly Coupled Fermions in Odd Dimensions and the Running Cut-off Λd. Am J Mod Phys. 2024;13(1):1-11. doi: 10.11648/j.ajmp.20241301.11

Copyright © 2024 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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