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

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.