# Casimir effect for nucleon parity doublets

## TL;DR

This paper investigates how finite-volume effects, modeled via the Casimir effect, influence chiral symmetry and nucleon masses in the parity-doublet model, revealing boundary-condition-dependent symmetry restoration or breaking.

## Contribution

It introduces the vacuum energy shift as a Casimir effect into the parity-doublet model to study finite-volume impacts on nucleon properties.

## Key findings

- Antiperiodic boundary conditions restore chiral symmetry at finite volume.
- Periodic boundary conditions enhance chiral symmetry breaking.
- Nucleon masses degenerate under antiperiodic boundary conditions.

## Abstract

Finite-volume effects for the nucleon chiral partners are studied within the framework of the parity-doublet model. Our model includes the vacuum energy shift for nucleons, which is the Casimir effect. We find that for the antiperiodic boundary the finite-volume effect leads to chiral symmetry restoration, and the masses of the nucleon parity doublets degenerate. For the periodic boundary, the chiral symmetry breaking is enhanced, and the masses of the nucleons also increase. We also discuss the finite-temperature effect and the dependence on the number of compactified spatial dimensions.