Nambu-Jona-Lasinio Model Coupled to Constant Electromagnetic Fields in D-Dimension

TL;DR

This paper studies the critical behavior and vacuum instability of the Nambu-Jona-Lasinio model in various dimensions when coupled to constant electromagnetic fields, revealing how electric and magnetic fields influence phase transitions and stability.

Contribution

It provides a nonperturbative analysis of the NJL model under electromagnetic fields across different dimensions, highlighting the effects of electric and magnetic fields on critical phenomena and vacuum stability.

Findings

Critical coupling in D=3 and 4 vanishes with infinitesimal magnetic fields.

Non-zero $F_{ ext{mu nu}} ilde{F}^{ ext{mu nu}}$ causes vacuum instability.

Asymptotic expansion matches exact values for critical quantities.

Abstract

Critical dynamics of the Nambu-Jona-Lasinio model, coupled to a constant electromagnetic field in D=2, 3, and 4, is reconsidered from a viewpoint of infrared behavior and vacuum instability. The latter is associated with constant electric fields and cannot be avoidable in the nonperturbative framework obtained through the proper time method. As for magnetic fields, an infrared cut-off is essential to investigate the critical phenomena. The result reconfirms the fact that the critical coupling in D=3 and 4 goes to zero even under an infinitesimal magnetic field. There also shows that a non-vanishing $F_{\mu\nu}\widetilde F^{\mu\nu}$ causes instability. A perturbation with respect to external fields is adopted to investigate critical quantities, but the resultant asymptotic expansion excellently matches with the exact value.