Critical Couplings in the Nambu--Jona-Lasinio Model with the Constant Electromagnetic Fields

TL;DR

This paper investigates the effects of constant electromagnetic fields on the critical couplings in the Nambu--Jona-Lasinio model across multiple dimensions, revealing that the critical coupling remains nonzero in three dimensions and confirming the accuracy of asymptotic expansion methods.

Contribution

It provides a comprehensive analysis of the Nambu--Jona-Lasinio model with external fields, correcting previous assumptions about the critical coupling in three dimensions and validating the asymptotic expansion approach.

Findings

Critical coupling remains nonzero in three dimensions.

Asymptotic expansion matches the exact value well.

Infrared cut-off is crucial for the proper time method.

Abstract

A detailed analysis is performed for the Nambu--Jona-Lasinio model coupled with constant (external) magnetic and/or electric fields in two, three, and four dimensions. The infrared cut-off is essential for a well-defined functional determinant by means of the proper time method. Contrary to the previous observation, the critical coupling remains nonzero even in three dimensions. It is also found that the asymptotic expansion has an excellent matching with the exact value.