Super-Strong Coupling NJL model in arbitrary space-time dimensions

TL;DR

This paper investigates chiral symmetry breaking in the NJL model across various space-time dimensions, revealing bifurcations and chaos in the super-strong coupling regime through a discrete dynamical system approach.

Contribution

It introduces an iterative dynamical system method to analyze the NJL model's gap equation in arbitrary dimensions, identifying bifurcations and chaotic behavior at strong couplings.

Findings

Critical coupling for symmetry breaking identified.

Bifurcation points lead to nontrivial solutions.

Chaotic dynamics emerge at super-strong coupling.

Abstract

We study chiral symmetry breaking in the Nambu--Jona-Lasinio model regularized in proper-time in arbitrary space-time dimensions through an iterative procedure by writing the gap equation in the form of a discrete dynamical system with the coupling constant as the control parameter. Expectedly, we obtain the critical coupling for chiral symmetry breaking when a nontrivial solution bifurcates away from the trivial one and becomes an attractor. By increasing further the value of the coupling constant, we observe a second bifurcation where the dynamical solution is no longer an attractor, and observation that holds true in all space-time dimensions. In the super-strong coupling regime, the system becomes chaotic.