Interacting fermions in rotation: chiral symmetry restoration, moment of inertia and thermodynamics

TL;DR

This paper investigates how rotation and finite temperature affect chiral symmetry, phase structure, and thermodynamics of fermionic matter within the NJL model, revealing boundary-induced effects and symmetry restoration phenomena.

Contribution

It introduces the impact of finite cylindrical boundaries on rotating fermionic matter, showing boundary effects on phase structure and chiral symmetry restoration at finite temperature.

Findings

Boundary conditions cause steplike oscillations in chiral condensate.

Rotation at finite temperature restores chiral symmetry.

Moment of inertia varies with chiral phase.

Abstract

We study rotating fermionic matter at finite temperature in the framework of the Nambu-Jona-Lasinio model. In order to respect causality the rigidly rotating system must be bound by a cylindrical boundary with appropriate boundary conditions that confine the fermions inside the cylinder. We show the finite geometry with the MIT boundary conditions affects strongly the phase structure of the model leading to three distinct regions characterized by explicitly broken (gapped), partially restored (nearly gapless) and spontaneously broken (gapped) phases at, respectively, small, moderate and large radius of the cylinder. The presence of the boundary leads to specific steplike irregularities of the chiral condensate as functions of coupling constant, temperature and angular frequency. These steplike features have the same nature as the Shubnikov-de Haas oscillations with the crucial difference that they occur in the absence of both external magnetic field and Fermi surface. At finite temperature the rotation leads to restoration of spontaneously broken chiral symmetry while the vacuum at zero temperature is insensitive to rotation ("cold vacuum cannot rotate"). As the temperature increases the critical angular frequency decreases and the transition becomes softer. A phase diagram in angular frequency-temperature plane is presented. We also show that at fixed temperature the fermion matter in the chirally restored (gapless) phase has a higher moment of inertia compared to the one in the chirally broken (gapped) phase.