Chiral Symmetry Breaking in the Nambu-Jona-Lasinio Model in External Constant Electromagnetic Field

TL;DR

This paper investigates how external constant electric and magnetic fields influence dynamical chiral symmetry breaking in the Nambu-Jona-Lasinio model across different dimensions, revealing that certain field invariants inhibit symmetry breaking.

Contribution

It provides a detailed analysis of the effects of electromagnetic field invariants on chiral symmetry breaking in the NJL model in various dimensions, highlighting the role of the second invariant.

Findings

In 3+1 dimensions, the critical coupling increases with the second invariant, inhibiting DχSB.

In 2+1 dimensions, the problem simplifies to purely electric or magnetic fields due to fewer invariants.

The second invariant of the electromagnetic field acts as an inhibitor of chiral symmetry breaking.

Abstract

Dynamical chiral symmetry breaking (D$\chi$SB) is studied in the Nambu-Jona-Lasinio model for an arbitrary combination of external constant electric and magnetic fields. In 3+1 dimensions it is shown that the critical coupling constant increases with increasing of the value of the second invariant of electromagentic field $\vec{E}\cdot\vec{B}$, i.e. the second invariant inhibits $D\chi SB$. The case of 2+1 dimensions is simpler because there is only one Lorentz invariant of electromagnetic field and any combination of constant fields can be reduced to cases either purely magnetic or purely electric field.