We study chiral symmetry breaking in the Nambu–Jona-Lasinio model regularized in proper time in arbitrary spacetime 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 spacetime dimensions. In the superstrong coupling regime, the system becomes chaotic.

• Received 3 May 2018

DOI:https://doi.org/10.1103/PhysRevD.98.054027

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Published by the American Physical Society