A Comparative Study of NJL and Sakai-Sugimoto Models

TL;DR

This paper compares the NJL and Sakai-Sugimoto models in terms of their mass generation and phase diagrams under various conditions, highlighting their similarities at low chemical potential and differences at high chemical potential.

Contribution

It provides a detailed comparison of the two models' responses to temperature, electromagnetic fields, and chemical potential, revealing their limitations and differences in capturing certain phenomena.

Findings

Models agree at low chemical potential

NJL shows de Haas-van Alphen oscillations at high chemical potential

Sakai-Sugimoto fails to reproduce Fermi sphere effects

Abstract

The Nambu-Jona-Lasinio and Sakai-Sugimoto models are juxtaposed, focusing on the models' dynamically generated masses and the phase diagrams. The models are studied in the parameter space of temperature, constant electromagnetic fields and the quark chemical potential. When the chemical potential is zero or small, the models show good agreement. However, the responses of the models under the large chemical potential are very different. In the presence of the background magnetic field, while the large chemical potential triggers the de Haas-van Alphen oscillation and the boundstate destabilization effect of the magnetic field in the NJL model, the Sakai-Sugimoto model completely fails to capture these phenomena, indicating the lack of the fermi sphere in the latter model. Also the orders of the chiral phase transitions are generally different.