# Effects of rotation and boundaries on chiral symmetry breaking of relativistic fermions

## TL;DR

This paper investigates how boundary conditions and rotation affect chiral symmetry breaking in relativistic fermions, revealing that the critical temperature for chiral restoration decreases with angular velocity and depends on boundary parameters.

## Contribution

It demonstrates the significant influence of boundary conditions on the phase structure of rotating relativistic fermions within the NJL model.

## Key findings

- Chiral restoration temperature decreases quadratically with angular velocity.
- Boundary conditions notably affect the phase diagram and critical temperature.
- The critical curve's position and slope depend on the chiral boundary parameter.

## Abstract

In order to avoid unphysical causality-violating effects any rigidly rotating system must be bounded in directions transverse to the axis of rotation. We demonstrate that this requirement implies substantial dependence of properties of relativistically rotating system on the boundary conditions. We consider a system of interacting fermions described by the Nambu-Jona-Lasinio model in a space bounded by cylindrical surface of finite radius. In order to confine the fermions inside the cylinder we impose "chiral" MIT boundary conditions on its surface. These boundary conditions are parameterized by a continuous chiral angle \Theta. We find that at any value of \Theta the chiral restoration temperature T_c decreases as a quadratic function of the angular frequency \Omega. However, the position and the slope of the critical curve T_c = T_c(\Omega) in the phase diagram depends noticeably on the value of the chiral angle.